
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 the 5 by 5 square grid, each dot is located 1 cm from its nearest horizontal and vertical neighbors as shown below. We have triangle $ABC$ defined as follows: $A$ is at (0,1), $B$ is at (4,4), and $C$ is at (4,0). Calculate the product of the area of triangle $ABC$ and the perimeter of triangle $ABC$. Express your answer in simplest radical form.

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