
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 \( ABC \), point \( P \) is positioned inside such that \( \angle PAC = 10^\circ \), \( \angle PCA = 20^\circ \), \( \angle PAB = 30^\circ \), and \( \angle ABC = 40^\circ \). What is the degree measure of \( \angle BPC \)?

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