
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 floor of a room has dimensions of $4 \times 5 \ \mathrm{m}^{2}$, and the ceiling height is 4 meters. A fly named Masha is sitting in one corner of the ceiling, while a spider named Petya is in the opposite corner of the ceiling. Masha decides to visit Petya by the shortest route, but she must touch the floor on her way. Find the length of the path she travels.

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