
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
Triangle $ABC$ has $AB=15$, $AC=17$, and $BC=8$. Points $F$ and $G$ are located on $\overline{AB}$ and $\overline{AC}$, respectively, such that $\overline{FG}$ is parallel to $\overline{BC}$ and contains the centroid of triangle $ABC$. Compute the length of $\overline{FG}$.

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