
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 from its nearest horizontal and vertical neighbors, calculate the product of the area of square \(EFGH\) and the perimeter of square \(EFGH\), where the vertices of square \(EFGH\) are located as follows on the grid:
- \(E\) at (1,5)
- \(F\) at (5,6)
- \(G\) at (6,2)
- \(H\) at (2,1)

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