
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 \( \triangle ABC \), \( G \) is the centroid, and the lengths of the sides opposite to the angles \( A \), \( B \), and \( C \) are \( a \), \( b \), and \( c \) respectively. Given that \( 56a \overrightarrow{GA} + 40b \overrightarrow{GB} + 35c \overrightarrow{GC} = \mathbf{0} \), find the angle \( \angle B \).

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