
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 6 by 6 square grid where each dot is 1 cm apart from its nearest horizontal and vertical neighbors, consider a right triangle with vertices labeled $P$, $Q$, and $R$. The vertices $P$, $Q$, and $R$ are located at coordinates $(1, 5)$, $(5, 5)$, and $(1, 1)$, respectively. What is the product of the area of triangle $PQR$ and the perimeter of triangle $PQR$? Express your answer in simplest form.

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