
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
In the pyramid \(ABCD\), points \(M\), \(F\), and \(K\) are the midpoints of edges \(BC\), \(AD\), and \(CD\) respectively. Points \(P\) and \(Q\) are chosen on lines \(AM\) and \(CF\) respectively such that \(PQ \parallel BK\). Find the ratio \(PQ : BK\).

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