
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
Given that $P$ is a point in the plane of $\triangle ABC$, and $\overrightarrow{PB}+ \overrightarrow{PC}+2 \overrightarrow{PA}=0$, if a soybean is randomly dropped inside $\triangle ABC$, the probability that the soybean falls inside $\triangle PBC$ is ______.

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