
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
Let \( ABCD \) be a parallelogram. Let \( E \) be the midpoint of \( AB \) and \( F \) be the midpoint of \( CD \). Points \( P \) and \( Q \) are on segments \( EF \) and \( CF \), respectively, such that \( A, P \), and \( Q \) are collinear. Given that \( EP = 5 \), \( PF = 3 \), and \( QF = 12 \), find \( CQ \).

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