
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 sells a batch of brand-name shirts, with an average daily sales of 20 pieces and a profit of $40 per piece. In order to expand sales and reduce inventory quickly, the mall decides to take appropriate price reduction measures. After investigation, it was found that if the price of each shirt is reduced by $1, the mall can sell 2 more pieces on average per day. Find:<br/>$(1)$ If the price of each shirt is reduced by $3, the average daily sales quantity will be ______ pieces;<br/>$(2)$ If the mall needs to make an average daily profit of $1200, how much should each shirt be reduced by?

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