
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 6 by 6 square grid below, each dot is 1 cm apart from its nearest horizontal and vertical neighbors. Calculate the product of the value of the area of square $EFGH$ and the value of the perimeter of square $EFGH$ (in cm). 
Position of points are: $E = (5,5), F = (5,1), G = (1,1), H = (1,5)$.
Express your answer in simplest radical form.

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