
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  $EP = 5$ ,  $P F = 3$ , and  $QF = 12$ , find  $CQ$ .

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