
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
A square $ABCD$ has a side length of 36 inches. An equilateral triangle $BFC$ with the same side length is cut from the square. This triangle is then rotated 180 degrees around point B and attached to create a new shaded region $ABFCDE$. Calculate the perimeter of this shaded region.

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