
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 a cell in a checkered paper is 1. A rectangle with sides \( m \) and \( n \) is constructed along the grid lines. Is it possible to draw a closed broken line along the grid lines in the rectangle that passes through each grid point located inside or on the boundary of the rectangle exactly once? If possible, what is its length?

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