
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
Alec must purchase 20 identical caps and only has $\$150$. There is a flat $\$3$ entrance fee for shopping at the warehouse store where he plans to buy the caps. The price of each cap is the same whole-dollar amount. Assuming a $7\%$ sales tax is added to the price of each cap, what is the greatest possible price (in dollars) of a cap that would allow Alec to buy the caps?

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