
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
On a 4 by 4 square grid, each dot is 2 cm from its nearest horizontal and vertical neighbors. Calculate the product of the area of square $PQRS$ (in cm$^2$) and the perimeter of square $PQRS$ (in cm), where $PQRS$ is formed by the vertices $P(1,3)$, $Q(4,4)$, $R(3,1)$, and $S(0,0)$.

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