
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
A regular triangular pyramid is intersected by a plane passing through a vertex of the base and the midpoints of two lateral edges. Find the ratio of the lateral surface area of the pyramid to the area of the base, given that the intersecting plane is perpendicular to one of the lateral faces (specify which one).

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