
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
The side of each square in a grid paper is 1 unit. A rectangle with sides \( m \) and \( n \) is constructed along the grid lines. Is it possible to draw a closed polygonal chain (broken line) along the grid lines within the rectangle such that it passes exactly once through each vertex of the grid located inside or on the boundary of the rectangle? If possible, what is its length?

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