
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, the shop decides to implement an appropriate price reduction strategy. Through surveys, it was found that for every $1$ yuan reduction in the price per pot, the flower shop can sell an additional $2$ pots on average per day. By how much should the price per pot be reduced to maximize the shop's average daily profit, and what would be the maximum daily profit?

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