
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 height of a right triangular prism is \( H \). A plane passes through the midline of the lower base and is parallel to the side of the upper base. This plane forms an acute dihedral angle \( \alpha \) with the plane of the lower base. Find the area of the cross-section formed by this plane.

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