deps(example): bump the dependencies group in /examples/nextjs-openai…

… with 2 updates (#2577)

Bumps the dependencies group in /examples/nextjs-openai with 2 updates: [ai](https://github.com/vercel/ai) and [openai](https://github.com/openai/openai-node).

Updates `ai` from 4.0.14 to 4.0.16
<details>
<summary>Release notes</summary>
<p><em>Sourced from <a href="https://github.com/vercel/ai/releases">ai's releases</a>.</em></p>
<blockquote>
<h2>[email protected]</h2>
<h3>Patch Changes</h3>
<ul>
<li>e3fac3f: fix (ai/core): change smoothStream default delay to 10ms</li>
</ul>
<h2>[email protected]</h2>
<h3>Patch Changes</h3>
<ul>
<li>cc16a83: feat (ai/core): add smoothStream helper</li>
<li>cc16a83: feat (ai/core): add experimental transform option to streamText</li>
</ul>
</blockquote>
</details>
<details>
<summary>Commits</summary>
<ul>
<li><a href="https://github.com/vercel/ai/commit/57f6e76c76d11de3458c46b5a09fc92b9822762d"><code>57f6e76</code></a> Version Packages (<a href="https://redirect.github.com/vercel/ai/issues/4080">#4080</a>)</li>
<li><a href="https://github.com/vercel/ai/commit/e3fac3fe8901b75b72475b5cacfb10c166005304"><code>e3fac3f</code></a> fix (ai/core): change smoothStream default delay to 10ms (<a href="https://redirect.github.com/vercel/ai/issues/4079">#4079</a>)</li>
<li><a href="https://github.com/vercel/ai/commit/b8c76a7563feb3b604d0e2df81501b4d76e05387"><code>b8c76a7</code></a> Version Packages (<a href="https://redirect.github.com/vercel/ai/issues/4076">#4076</a>)</li>
<li><a href="https://github.com/vercel/ai/commit/cc16a830c65073d60d5403835c9a8d762589f066"><code>cc16a83</code></a> feat (ai/core): add experimental transform option to streamText (<a href="https://redirect.github.com/vercel/ai/issues/4074">#4074</a>)</li>
<li><a href="https://github.com/vercel/ai/commit/3ce210fcee79153c6293104c896efef0fd9ece84"><code>3ce210f</code></a> docs: fix image gen title (<a href="https://redirect.github.com/vercel/ai/issues/4075">#4075</a>)</li>
<li><a href="https://github.com/vercel/ai/commit/56290aff39699f1bf57afd8499e854fd64c4411c"><code>56290af</code></a> feat (docs): add OpenRouter AI provider documentation (<a href="https://redirect.github.com/vercel/ai/issues/4073">#4073</a>)</li>
<li><a href="https://github.com/vercel/ai/commit/e10a3ef465b9235c192ab5e5736fb434edacfd80"><code>e10a3ef</code></a> Version Packages (<a href="https://redirect.github.com/vercel/ai/issues/4065">#4065</a>)</li>
<li><a href="https://github.com/vercel/ai/commit/c0b1c7eca391859d488ddc5e07d0084a77967094"><code>c0b1c7e</code></a> feat (provider/google): Add Gemini 2.0 model. (<a href="https://redirect.github.com/vercel/ai/issues/4064">#4064</a>)</li>
<li><a href="https://github.com/vercel/ai/commit/03e4f4795ab15a3eedebeb2641556a26139e230c"><code>03e4f47</code></a> docs: add image generation chatbot recipe (<a href="https://redirect.github.com/vercel/ai/issues/4063">#4063</a>)</li>
<li><a href="https://github.com/vercel/ai/commit/320cc0e62807f2c6ad0b18df78bb073ccc28ddbc"><code>320cc0e</code></a> Version Packages (<a href="https://redirect.github.com/vercel/ai/issues/4060">#4060</a>)</li>
<li>Additional commits viewable in <a href="https://github.com/vercel/ai/compare/[email protected]@4.0.16">compare view</a></li>
</ul>
</details>
<br />

Updates `openai` from 4.76.1 to 4.76.2
<details>
<summary>Release notes</summary>
<p><em>Sourced from <a href="https://github.com/openai/openai-node/releases">openai's releases</a>.</em></p>
<blockquote>
<h2>v4.76.2</h2>
<h2>4.76.2 (2024-12-12)</h2>
<p>Full Changelog: <a href="https://github.com/openai/openai-node/compare/v4.76.1...v4.76.2">v4.76.1...v4.76.2</a></p>
<h3>Chores</h3>
<ul>
<li><strong>internal:</strong> update isAbsoluteURL (<a href="https://redirect.github.com/openai/openai-node/issues/1223">#1223</a>) (<a href="https://github.com/openai/openai-node/commit/e908ed759996fb7706baf46d094fc77419423971">e908ed7</a>)</li>
<li><strong>types:</strong> nicer error class types + jsdocs (<a href="https://redirect.github.com/openai/openai-node/issues/1219">#1219</a>) (<a href="https://github.com/openai/openai-node/commit/576d24cc4b3d766dfe28a6031bdc24ac1b711655">576d24c</a>)</li>
</ul>
</blockquote>
</details>
<details>
<summary>Changelog</summary>
<p><em>Sourced from <a href="https://github.com/openai/openai-node/blob/master/CHANGELOG.md">openai's changelog</a>.</em></p>
<blockquote>
<h2>4.76.2 (2024-12-12)</h2>
<p>Full Changelog: <a href="https://github.com/openai/openai-node/compare/v4.76.1...v4.76.2">v4.76.1...v4.76.2</a></p>
<h3>Chores</h3>
<ul>
<li><strong>internal:</strong> update isAbsoluteURL (<a href="https://redirect.github.com/openai/openai-node/issues/1223">#1223</a>) (<a href="https://github.com/openai/openai-node/commit/e908ed759996fb7706baf46d094fc77419423971">e908ed7</a>)</li>
<li><strong>types:</strong> nicer error class types + jsdocs (<a href="https://redirect.github.com/openai/openai-node/issues/1219">#1219</a>) (<a href="https://github.com/openai/openai-node/commit/576d24cc4b3d766dfe28a6031bdc24ac1b711655">576d24c</a>)</li>
</ul>
</blockquote>
</details>
<details>
<summary>Commits</summary>
<ul>
<li><a href="https://github.com/openai/openai-node/commit/6608f957b62a734c93c006bade5e3b0b8b577c4c"><code>6608f95</code></a> release: 4.76.2</li>
<li><a href="https://github.com/openai/openai-node/commit/f13fed4137bbbe2e6e0a83c1820ccdeecb6ddf01"><code>f13fed4</code></a> chore(internal): update isAbsoluteURL (<a href="https://redirect.github.com/openai/openai-node/issues/1223">#1223</a>)</li>
<li><a href="https://github.com/openai/openai-node/commit/94ef9d75f20699e80c81fb0defd31dc62d8d3585"><code>94ef9d7</code></a> chore(types): nicer error class types + jsdocs (<a href="https://redirect.github.com/openai/openai-node/issues/1219">#1219</a>)</li>
<li>See full diff in <a href="https://github.com/openai/openai-node/compare/v4.76.1...v4.76.2">compare view</a></li>
</ul>
</details>
<br />


Dependabot will resolve any conflicts with this PR as long as you don't alter it yourself. You can also trigger a rebase manually by commenting `@dependabot rebase`.

[//]: # (dependabot-automerge-start)
[//]: # (dependabot-automerge-end)

---

<details>
<summary>Dependabot commands and options</summary>
<br />

You can trigger Dependabot actions by commenting on this PR:
- `@dependabot rebase` will rebase this PR
- `@dependabot recreate` will recreate this PR, overwriting any edits that have been made to it
- `@dependabot merge` will merge this PR after your CI passes on it
- `@dependabot squash and merge` will squash and merge this PR after your CI passes on it
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- `@dependabot reopen` will reopen this PR if it is closed
- `@dependabot close` will close this PR and stop Dependabot recreating it. You can achieve the same result by closing it manually
- `@dependabot show <dependency name> ignore conditions` will show all of the ignore conditions of the specified dependency
- `@dependabot ignore <dependency name> major version` will close this group update PR and stop Dependabot creating any more for the specific dependency's major version (unless you unignore this specific dependency's major version or upgrade to it yourself)
- `@dependabot ignore <dependency name> minor version` will close this group update PR and stop Dependabot creating any more for the specific dependency's minor version (unless you unignore this specific dependency's minor version or upgrade to it yourself)
- `@dependabot ignore <dependency name>` will close this group update PR and stop Dependabot creating any more for the specific dependency (unless you unignore this specific dependency or upgrade to it yourself)
- `@dependabot unignore <dependency name>` will remove all of the ignore conditions of the specified dependency
- `@dependabot unignore <dependency name> <ignore condition>` will remove the ignore condition of the specified dependency and ignore conditions


</details>

examples/nextjs-openai/package.json

@@ -11,9 +11,9 @@
   "dependencies": {
     "@ai-sdk/openai": "^1.0.8",
     "@arcjet/next": "file:../../arcjet-next",
-    "ai": "^4.0.14",
+    "ai": "^4.0.16",
     "next": "15.1.0",
-    "openai": "^4.76.1",
+    "openai": "^4.76.2",
     "openai-chat-tokens": "^0.2.8",
     "react": "^19",
     "react-dom": "^19"