
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 pyramid \( S A B C D \) is a rectangle \( A B C D \), and its height is the edge \( S A = 25 \). Point \( P \) lies on the median \( D M \) of face \( S C D \), point \( Q \) lies on the diagonal \( B D \), and lines \( A P \) and \( S Q \) intersect. Find the length of \( P Q \) if \( B Q : Q D = 3 : 2 \).

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