
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 a regular hexagonal prism, a plane is drawn through a side of the base and the midpoint of the segment connecting the centers of the bases. This plane makes an acute angle $\alpha$ with the base plane. Find the area of the section formed by this plane if the side of the base of the prism is $a$.

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