
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 quadrilateral pyramid \( MABCD \) is the parallelogram \( ABCD \). Point \( K \) bisects edge \( DM \). Point \( P \) lies on edge \( BM \) such that \( BP: PM = 1: 3 \). The plane \( APK \) intersects edge \( MC \) at point \( X \). Find the ratio of segments \( MX \) and \( XC \).

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