
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 a height of \( PO \), where \( M \) is the midpoint of \( PO \). A plane parallel to edge \( BC \) is drawn through \( AM \), dividing the pyramid into upper and lower parts. Find the ratio of the volumes of these two parts.

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