docs: add start-work actions to the Choose a source table (#676)

Co-authored-by: warp-agent-staging[bot] <240773466+warp-agent-staging[bot]@users.noreply.github.com>
Co-authored-by: Rachael Rose Renk <91027132+rachaelrenk@users.noreply.github.com>
Co-authored-by: Hong Yi Chen <hongyi@warp.dev>

Author: 3 people

src/content/docs/factories/connect-your-factory.mdx

@@ -15,16 +15,18 @@ Each source feeds into this factory's repositories. If the work belongs to a dif
 
 Pick the sources that match where work starts for your team. You can connect multiple sources, but not both Linear and Jira at the same time. The setup wizard currently offers Linear; to use Jira, connect it after setup or in your [factory definition](/factories/factory-as-code/).
 
-| Source | Best for | Continues in |
-| --- | --- | --- |
-| [Slack](/factories/integrations/slack/) | Chat and support requests | The Slack thread or DM |
-| [GitHub](/factories/integrations/github/) | Issues, pull requests, reviews, and CI | The issue, pull request, or review thread |
-| [GitLab](/factories/integrations/gitlab/) | Merge request activity and bot mentions | The merge request thread |
-| [Linear](/factories/integrations/linear/) | Planned issues | The Linear issue and its agent session |
-| [Jira](/factories/integrations/jira/) | Work items assigned to Warp | The Jira agent session |
-| [Factory API](/factories/factory-api/) | Custom integrations and scripts that dispatch by factory UID | The factory work item |
-| [Factory MCP](/factories/factory-mcp/) | Exchanging work with a local coding agent, in both directions | The factory work item |
-| Direct runs and schedules | One-off or recurring work | The factory work item |
+Once a source is connected, here's the concrete action that hands it work — each links to that integration's full instructions rather than repeating them.
+
+| Source | Best for | Start work by | Continues in |
+| --- | --- | --- | --- |
+| [Slack](/factories/integrations/slack/) | Chat and support requests | [Mentioning the app in a channel, thread, or DM](/factories/integrations/slack/#start-and-continue-work-from-slack) | The Slack thread or DM |
+| [GitHub](/factories/integrations/github/) | Issues, pull requests, reviews, and CI | [Adding the factory's label and mentioning **@warp-factory**](/factories/integrations/github/#mention-the-factory) | The issue, pull request, or review thread |
+| [GitLab](/factories/integrations/gitlab/) | Merge request activity and bot mentions | [Mentioning the factory's bot in a merge request comment](/factories/integrations/gitlab/#mention-the-factory) | The merge request thread |
+| [Linear](/factories/integrations/linear/) | Planned issues | [Assigning the issue to the factory, or mentioning the Warp app in a comment](/factories/integrations/linear/#route-agent-sessions) | The Linear issue and its agent session |
+| [Jira](/factories/integrations/jira/) | Work items assigned to Warp | [Assigning or mentioning **Warp** on a work item](/factories/integrations/jira/#connect-jira-and-add-an-automation) | The Jira agent session |
+| [Factory API](/factories/factory-api/) | Custom integrations and scripts that dispatch by factory UID | [Calling `POST /factory/{uid}/runs` with a prompt](/factories/factory-api/#dispatch-a-run-to-a-factory) | The factory work item |
+| [Factory MCP](/factories/factory-mcp/) | Exchanging work with a local coding agent, in both directions | [Calling `send_task` from a connected coding agent](/factories/factory-mcp/#send-new-work-to-a-factory) | The factory work item |
+| Direct runs and schedules | One-off or recurring work | [Clicking **New** on the factory's Runs page, or adding a schedule trigger](#direct-runs-and-schedules) | The factory work item |
 
 ## Connect a source