
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
A shop is planning to sell a new gadget. Their market research indicates that if the gadget is priced at $p$ dollars, where $p \leq 40$, then the number of gadgets expected to sell monthly is $200 - 4p$. Determine the price $p$ that maximizes the shop's revenue.

Present the answer in LaTex format: \boxed{Your answer}
user