
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 triangular pyramid, a plane passes through a side of the base and is perpendicular to the opposite lateral edge. Find the area of the resulting section if the base side length is \(a\) and the height of the pyramid is \(h\).

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