
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  $ABC$  be a triangle. Let  $X$  be the point on side  $AB$  such that  $\angle{BXC} = 60^{\circ}$ . Let  $P$  be the point on segment  $CX$  such that  $BP\bot AC$ . Given that  $AB = 6, AC = 7,$  and  $BP = 4,$  compute  $CP$ .

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