Getting “no action argument defined” on webhook

I’ve now got the webhook responding to posts. However, even though my add_filter function completes successfully I have two problems.

1. The response from the webhook is always:

{
    "success": false,
    "action": "custom_action",
    "msg": "It looks like your current webhook call has no action argument defined, it is deactivated or it does not have any action function."
}

2. I can’t figure out how to put in my own response to the webhook so that the calling site can get data back.

How do I fix these?