
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 side of the base of a regular triangular pyramid is \(a\), and the dihedral angle at the base is \(\alpha\). The pyramid is cut by a plane parallel to the base. The area of the cross-section is equal to the lateral surface area of the resulting truncated pyramid. Find the distance from the cutting plane to the base of the pyramid.

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