
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 pyramid is intersected by a plane parallel to its base, dividing its lateral surface into two parts of equal area. In what ratio does this plane divide the lateral edges of the pyramid?

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