
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
If the area and perimeter of a square both change with the length of the side, calculate the instantaneous rate of change of the area with respect to the perimeter when the side length of the square is $3cm$.

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