
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 \(4 \times 4\) square is divided into 16 \(1 \times 1\) squares. Define a path as a movement along the sides of unit squares, where no side is traversed more than once. What is the maximum length of a path connecting two opposite vertices of the large square?

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