
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
A circle has radius  $52$  and center  $O$ .  Points  $A$  is on the circle, and point  $P$  on  $\overline{OA}$  satisfies  $OP = 28$ .  Point  $Q$  is constructed such that  $QA = QP = 15$ , and point  $B$  is constructed on the circle so that  $Q$  is on  $\overline{OB}$ . Find  $QB$ .

*Proposed by Justin Hsieh*

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