
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 coffee shop is deciding what price it should charge for a special blend of coffee per cup. After conducting market research, the shop finds that if they set the price at $p$ dollars (where $p \le 30$), then the number of cups sold per month can be modeled by $150 - 4p$. The shop also has a fixed monthly cost of $200 for the special blend ingredients. Determine the price per cup that maximizes the shop's monthly profit.

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