
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 $PQR$, $PQ = 17$, $PR = 19$, and $QR = 20$. Let $J$ be the incenter. The incircle of triangle $PQR$ touches sides $QR$, $PR$, and $PQ$ at $D$, $E$, and $F$, respectively. Find the length of $QJ$.

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