
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 the sides opposite to angles A, B, and C are denoted as a, b, and c respectively. If $a \overrightarrow {GA} + \frac {3}{5}b \overrightarrow {GB} + \frac {3}{7}c \overrightarrow {GC} = \overrightarrow {0}$, then find the measure of $\angle C$.

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