
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 certain shopping mall purchased a batch of daily necessities at a unit price of $20$ yuan. If they are sold at a unit price of $30$ yuan, then 400 items can be sold in half a month. According to sales experience, increasing the selling price will lead to a decrease in sales volume. Specifically, for every $1$ yuan increase in selling price, the sales volume decreases by $20$ items. What is the unit price at which the sales volume is maximized in half a month?

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