
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
Given a store sells a batch of helmets for $80$ yuan each, and can sell $200$ helmets per month, with a cost price of each helmet being $50$ yuan, and for every $1$ yuan reduction in price, an additional $20$ helmets can be sold per month, determine the selling price per helmet when the store maximizes its monthly profit.

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