
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
In the picture, there is a polyhedron and all its dihedral angles are right angles. Sasha claims that the shortest path on the surface of this polyhedron from vertex \( X \) to vertex \( Y \) is 4.5 units. Is he right?

![Polyhedron](https://cdn.mathpix.com/cropped/2024_05_06_c3e6e773b77df3772054g-07.jpg?height=382&width=474&top_left_y=106&top_left_x=1408)

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