
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 fly trapped inside a rectangular prism with sides $1$ meter, $\sqrt{2}$ meters, and $\sqrt{3}$ meters decides to relieve its boredom by visiting each corner of the prism. It starts and ends at the same corner, visiting each of the other corners exactly once directly. Find the maximum possible length of its path.

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