
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
 $\triangle KWU$  is an equilateral triangle with side length  $12$ . Point  $P$  lies on minor arc  $\overarc{WU}$  of the circumcircle of  $\triangle KWU$ . If  $\overline{KP} = 13$ , find the length of the altitude from  $P$  onto  $\overline{WU}$ .

*Proposed by Bradley Guo*

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