
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 $G$ be the centroid of $\triangle ABC$, and let $a$, $b$, and $c$ be the lengths of the sides opposite to angles $A$, $B$, and $C$ respectively, find the measure of angle $A$ if $a \overrightarrow{GA}+b \overrightarrow{GB}+ \dfrac{\sqrt{3}}{3}c \overrightarrow{GC}= \overrightarrow{0}$.

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