
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
In triangle $PQR$, $PQ = 20$, $PR = 21$, and $QR = 19$. Points $F$ and $G$ are on $PQ$ and $PR$ respectively, such that line $FG$ is parallel to $QR$ and passes through the centroid of triangle $PQR$. Find the length of $FG$ in the simplest form $a/b$, where $a$ and $b$ are co-prime integers. Find $a+b$.

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