
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

On the lateral edges \(AA_1\), \(BB_1\), and \(CC_1\) of a triangular prism \(ABC A_1 B_1 C_1\), points \(M\), \(N\), and \(P\) are located respectively such that \(AM: AA_1 = B_1N: BB_1 = C_1P: CC_1 = 3:4\). On the segments \(CM\) and \(A_1N\), points \(E\) and \(F\) are located respectively such that \(EF \parallel B_1P\). Find the ratio \(EF : B_1P\).

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