FreePBX to custom CRM

We have a custom CRM, made with Codeigniter. We need to connect our FreePBX to CRM so when the user see a lead he just push on the phone number and can make the call. Also we want to record all calls and must be available on the lead data. The supervisor can audit the calls very easy.
Also we need that FreePBX make the calls automatically and must show the seller which lead is calling.