
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 box with dimensions $1 \times 1 \times 2$ meters decides to visit each corner of the box, starting and ending at the same corner and visiting each of the other corners exactly once. The fly must follow the longest path possible but must use exactly two face diagonals and one space diagonal in its path. Calculate the maximum possible length, in meters, of its path.

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