
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 \(\triangle ABC\), \(AB = 2\), \(BC = \sqrt{3}\), and \(\angle ABC = 150^\circ\). \(P\) is a point on the plane such that \(\angle APB = 45^\circ\) and \(\angle BPC = 120^\circ\). Find \(BP\).

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