
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 in triangle $\triangle ABC$ the internal angles are $A$, $B$, and $C$, and the centroid is $G$. If $2\sin A \overrightarrow{GA} + \sqrt{3}\sin B \overrightarrow{GB} + 3\sin C \overrightarrow{GC} = \overrightarrow{0}$, express $\cos B$ in terms of known values.

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