Simplify agent tools docs (#1012)

* Simplify agent tools docs

* Fix input

pages/docs/agent-kit/ai-agents-tools.mdx

@@ -66,16 +66,11 @@ Agents themselves are relatively simple.  When you call `run` on an agent, there
     * The agent’s `onFinish` lifecycle is called with the new result.  This lets you inspect the output of tool use
 5. The result is returned to the caller
 
-## Agent tools
-
-When you create an agent you can specify any number of tools that the agent can use. Tools follow the standard formats that OpenAI and Anthropic provide: a name and a description, plus typed parameters.
-
-In AgentKit, you also define a `handler` function which is called when the tool is invoked.  Because AgentKit runs in the backend (on your own infrastructure) these handlers can run almost any code you define.
-
+## Agent system prompts
 
-### Complex agents with tools
+You can define an agent's system prompt as a string or as an async callback which can inspect network state and return custom instructions.  This is useful in an agentic workflow:  multiple models are called in a loop, impacting network state that can adjust prompts.
 
-A more complex agent used in a network defines a description, lifecycle hooks, tools, and a dynamic set of instructions based off of network state:
+Here's an example:
 
 ```ts
 import { Agent, Network, agenticOpenai as openai } from "@inngest/agent-kit";
@@ -93,9 +88,7 @@ const agent = createAgent({
   // system defines a system prompt.  This function is called by the network each time
   // the agent runs, and allows you to customize the instructions based off of past state.
   system: async ({ network }) => {
-
-    // Each time this agent runs, it may produce "file" content.  Check if any
-    // content has already been produced in an agentic workflow.
+    // Inspect the network state to see if we have any existing code saved as files.
     const files: Record<string, string> | undefined = network?.state.kv.get("files")
     if (files === undefined) {
       return systemPrompt;
@@ -109,6 +102,45 @@ const agent = createAgent({
     }
     return prompt;
   },
+});
+
+```
+
+
+## Agent tools
+
+<Callout variant="info">
+  Tools are a vital part of agents, and have two core uses:
+
+    * Tools are exceptional at turn unstructured inputs into structured responses
+    * Tools can call arbitrary code, allowing models to interact with other systems
+</Callout>
+
+When you create an agent you can specify any number of tools that the agent can use. Tools follow the standard formats that OpenAI and Anthropic provide: a name and a description, plus typed parameters.
+
+In AgentKit, you also define a `handler` function which is called when the tool is invoked.  Because AgentKit runs in the backend (on your own infrastructure) these handlers can run almost any code you define.
+
+
+### Complex agents with tools
+
+A more complex agent used in a network defines a description, lifecycle hooks, tools, and a dynamic set of instructions based off of network state:
+
+```ts
+import { Agent, Network, agenticOpenai as openai } from "@inngest/agent-kit";
+
+const systemPrompt =
+    "You are an expert TypeScript programmer.  Given a set of asks, think step-by-step to plan clean, " +
+    "idiomatic TypeScript code, with comments and tests as necessary."
+
+const agent = createAgent({
+  name: "Code writer",
+
+  // description helps LLM routers choose the right agents to run.
+  description: "An expert TypeScript programmer which can write and debug code",
+
+  // system defines a system prompt.  This function is called by the network each time
+  // the agent runs, and allows you to customize the instructions based off of past state.
+  system: systemPrompt;
 
   // tools are provided to the model and are automatically called.
   tools: [
@@ -136,11 +168,6 @@ const agent = createAgent({
   ],
 });
 
-// Use this agent in a network of other agents, or with long-term state.
-const network = createNetwork({
-  agents: [agent]
-});
-
 ```
 
 Calling `.run` on this agent will pass the tools into your provider, allowing the model to select whether to run the `write_files` tool as a result.  Tools are automatically called on your behalf.

pages/docs/agent-kit/overview.mdx

@@ -55,7 +55,7 @@ export default inngest.createFunction(
     const input = `Classify then summarize the latest 10 blog posts
       on https://www.deeplearning.ai/blog/`
 
-    const result = await network.run(, ({ network }) => {
+    const result = await network.run(input, ({ network }) => {
       // Use an agent which figures out the specific agent to call
       // based off of the network's history.
       return defaultRoutingAgent;