Inbound and Outbound using the same Assistant

I have some really good prompts for Inbound Calls, but when the assistant needs to make calls, these prompts don't work properly.

Example: When receiving a call, the first question is full name. But after the lead fill up a form for estimate, the AI Assistant will call the lead and it should not ask for this information. Actually, it should say something like "Am I speaking with [Full Name] ?"

What do I need to do so both call types work fine at the same assistant? Is it a good prompt enough? What other resources should I use? Context? Pre-call webhook?

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