For outbound: I create, what is called a transient agent (created on thy fly using the API) in a make.com scenario. So to infuse information like calendar open slots I would get the open slots before I create the transient agent and then add the open calendar slots information in the prompt for the transient agent. Ensure that you include the current date in the prompt otherwise the agent will not act correctly.
what is the issue you're experiencing with your agent checking your calendar availability? Maybe it is easier to fix that part....