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

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