
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 product with a purchase price of $70$ yuan is sold at a retail price of $100$ yuan each by Dongfang Department Store. When sold at this price, the store can sell $20$ units per day. If the retail price of this product is reduced by $1$ yuan within a certain range, the daily sales volume will increase by $1$ unit. In order to maximize profit, the price should be reduced by ______ yuan.

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