
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
How many times do we need to lift the pencil if we want to draw a chessboard grid (its perimeter and internal lines) on a sheet of paper, if we are only allowed to traverse each line once?

If we can traverse segments multiple times, what is the shortest path to cover the entire grid without lifting the pencil? The perimeter of the board is $128 \mathrm{~cm}$.

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