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

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