feat(ai): Add OpenAI Completions and Responses API providers

- Implement OpenAICompletionsLLM for Chat Completions API with streaming
- Implement OpenAIResponsesLLM for Responses API with reasoning support
- Update types to use LLM/Context instead of AI/Request
- Add support for reasoning tokens, tool calls, and streaming
- Create test examples for both OpenAI providers
- Update Anthropic provider to match new interface

packages/ai/test/examples/openai-responses.ts

@@ -0,0 +1,60 @@
+import chalk from "chalk";
+import { OpenAIResponsesLLMOptions, OpenAIResponsesLLM } from "../../src/providers/openai-responses.js";
+import type { Context, Tool } from "../../src/types.js";
+
+// Define a simple calculator tool
+const tools: Tool[] = [
+    {
+        name: "calculate",
+        description: "Perform a mathematical calculation",
+        parameters: {
+            type: "object" as const,
+            properties: {
+                expression: {
+                    type: "string",
+                    description: "The mathematical expression to evaluate"
+                }
+            },
+            required: ["expression"]
+        }
+    }
+];
+
+const ai = new OpenAIResponsesLLM("gpt-5");
+const context: Context = {
+    messages: [
+        {
+            role: "user",
+            content: "Think about birds briefly. Then give me a list of 10 birds. Finally, calculate 42 * 17 + 123 and 453 + 434 in parallel using the calculator tool.",
+        }
+    ],
+    tools,
+}
+
+const options: OpenAIResponsesLLMOptions = {
+    onText: (t) => process.stdout.write(t),
+    onThinking: (t) => process.stdout.write(chalk.dim(t)),
+    reasoningEffort: "low",
+    reasoningSummary: "auto"
+};
+let msg = await ai.complete(context, options)
+context.messages.push(msg);
+console.log();
+console.log(chalk.yellow(JSON.stringify(msg, null, 2)));
+
+for (const toolCall of msg.toolCalls || []) {
+    if (toolCall.name === "calculate") {
+        const expression = toolCall.arguments.expression;
+        const result = eval(expression);
+        context.messages.push({
+            role: "toolResult",
+            content: `The result of ${expression} is ${result}.`,
+            toolCallId: toolCall.id,
+            isError: false
+        });
+    }
+}
+
+msg = await ai.complete(context, options);
+console.log();
+console.log(chalk.yellow(JSON.stringify(msg, null, 2)));