
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
Let \( P-ABC \) be a regular triangular pyramid with height \( PO \). M is the midpoint of \( PO \). A plane through \( AM \) is parallel to edge \( BC \), dividing the pyramid into two parts. Find the volume ratio of these two parts.

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