
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 grid paper, a rectangle composed of 72 squares is selected. Next, a closed polygonal line is drawn along the grid lines such that it passes through each grid point inside or on the boundary of the rectangle exactly once and does not exit the rectangle. What can be the area of the polygon enclosed by this polygonal line?

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