
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 point O is the centroid of triangle ABC, with the sides opposite to angles A, B, and C being of lengths a, b, and c respectively, and $2a \overrightarrow{OA} + b \overrightarrow{OB} + \frac{2\sqrt{3}}{3}c \overrightarrow{OC} = \overrightarrow{0}$, determine the ratio of $\sin A : \sin B : \sin C$.

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