
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 \( \overline{AB} \) such that \( \angle BXC = 60^\circ \). Let \( P \) be the point on segment \( \overline{CX} \) such that \( BP \perp AC \). Given that \( AB = 6 \), \( AC = 7 \), and \( BP = 4 \), compute \( CP \).

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