Your goal is to generate two things:

First, generate a python function named `gen_plan` that can take any continuous inputs. No list inputs are allowed.
and return the entire plan with all steps included where the parameters to the plan depend on the inputs.

Second, generate a python function `gen_initial_guess` that returns a set of initial guesses for the continuous input parameters. The number of initial guesses in the
`gen_initial_guess` should exactly match the number of inputs to the function excluding the state input.

The main function should be named EXACTLY `gen_plan` and the initial_guess of the main function should be named EXACTLY `gen_initial_guess`. Do not change the names. Do not create any additional classes or overwrite any existing ones.
Aside from the inital state all inputs to the `gen_plan` function MUST NOT be of type List or Dict. List and Dict inputs to `gen_plan` are not allowed.
