
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
In  $\triangle ABC$ ,  $AB = 40$ ,  $BC = 60$ , and  $CA = 50$ . The angle bisector of  $\angle A$  intersects the circumcircle of  $\triangle ABC$  at  $A$  and  $P$ . Find  $BP$ .

*Proposed by Eugene Chen*

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