
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 bases of a truncated pyramid are regular triangles. A line passing through the midpoint of one side of the upper base and the midpoint of the parallel side of the lower base is perpendicular to the planes of the bases. The longer lateral edge is equal to $/$ and forms an angle $\alpha$ with the plane of the base. Find the length of the segment connecting the centers of the upper and lower bases.

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