
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
On the lateral edge \( SB \) of the regular hexagonal pyramid \( SABCD \), a point \( P \) is selected such that \( SP \) is 10 times larger than \( PB \). The pyramid is divided into two parts by a plane passing through point \( P \) and parallel to the edges \( SE \) and \( FE \). Find the ratio of the volume of the larger part to the volume of the smaller part. If necessary, round the answer to the nearest hundredth.

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