
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
Construct the cross-section of the prism such that it is a trapezoid $D K M N$. Find the area of the projection of the cross-section onto the base plane of the prism and the cosine of the angle $\alpha$ between the cross-sectional plane and the base plane. Calculate the area $S_{ce4}$ of the cross-section.


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