
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 $G$ is the centroid of $\triangle ABC$, and $(56\sin A)\overrightarrow{GA}+(40\sin B)\overrightarrow{GB}+(35\sin C)\overrightarrow{GC}=\vec{0}$, determine the magnitude of $\angle B$.

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