
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 base of a pyramid is an equilateral triangle with a side length of \( a \). One of the lateral faces, which is perpendicular to the base plane, is also an equilateral triangle. Find the lateral surface area of the pyramid.

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