
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 plane is drawn through the vertex of the base and the midpoints of two lateral edges of a regular triangular pyramid. Find the ratio of the lateral surface area of the pyramid to the area of its base, given that the cutting plane is perpendicular to one of the lateral faces.

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