
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
The base of the pyramid \( PABCD \) is a parallelogram \( ABCD \). Point \( K \) is the midpoint of the edge \( CP \), and point \( M \) is located on the edge \( AB \) such that \( AM : MB = 1 : 2 \). Construct the cross-section of the pyramid with a plane passing through points \( K \) and \( M \) parallel to the line \( BD \). In what ratio does this plane divide the volume of the pyramid?

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