feat(bot,frontend,backend): add integration with external collaborative solver

frontend/src/lib/utils/markdown.ts

@@ -0,0 +1,19 @@
+import { Marked } from 'marked';
+
+const marked = new Marked({ breaks: true, gfm: true });
+
+export function processLatex(text: string): string {
+	return text
+		.replace(/\$\$(.*?)\$\$/gs, (_, tex) => {
+			const encoded = encodeURIComponent(tex.trim());
+			return `<img src="/service/latex?tex=${encoded}&display=1" alt="LaTeX" class="block my-1 max-h-12" />`;
+		})
+		.replace(/\$(.+?)\$/g, (_, tex) => {
+			const encoded = encodeURIComponent(tex.trim());
+			return `<img src="/service/latex?tex=${encoded}" alt="LaTeX" class="inline-block align-middle max-h-4" />`;
+		});
+}
+
+export function processContent(text: string): string {
+	return marked.parse(processLatex(text)) as string;
+}