
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]


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The base of the pyramid \( P ABCD \) is a parallelogram \( ABCD \). Points \( K \) and \( M \) are taken on the edges \( AB \) and \( PC \) respectively, such that \( AK:KB = CM:MP = 1:2 \). In what ratio does the plane passing through points \( K \) and \( M \) parallel to the line \( BD \) divide the volume of the pyramid \( P ABCD \)?

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