
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 flower shop sells a batch of expensive flowers, with an average daily sales volume of $20$ pots. Each pot generates a profit of $40$ yuan. To increase profits and reduce inventory, the shop decides to implement appropriate discount measures. Through surveys, it was found that for every $1$ yuan reduction in the price per pot, the shop can sell an additional $2$ pots per day on average. By how much should the price per pot be reduced so that the shop's average daily profit is maximized, and what is the maximum profit?

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