Caller: "This is a complex tax question, can you bring in a specialist?"
Agent: "Absolutely, I'll connect our tax specialist now. Please hold briefly."
-> Agent calls start_conference
-> Supervisor's phone rings, they join the call
Agent: "I have our tax specialist on the line. They can hear our conversation."

{
  "conferenceCallingEnabled": true,
  "conferenceMaxParticipants": 3,
  "conferenceSupervisorNumber": "+14155551234"
}

Parameters:
  reason: string (why the third party is being added)

Returns: "Conference started. Adding +1415555**** to the call."

curl -X POST https://api.thinnest.ai/v1/agents \
  -H "Authorization: Bearer $THINNESTAI_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "name": "Support Agent with Conference",
    "model": "gpt-4o",
    "instructions": "You are a support agent. If the caller needs specialized help, use start_conference to bring in a specialist. Always inform the caller before adding someone.",
    "voiceEnabled": true,
    "transcriber": { "provider": "deepgram", "model": "nova-2-conversationalai" },
    "voice": { "provider": "deepgram", "voiceId": "aura-2-thalia-en" },
    "conferenceCallingEnabled": true,
    "conferenceMaxParticipants": 3,
    "conferenceSupervisorNumber": "+14155551234"
  }'