
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 $\triangle{PQR}$ with $PQ = 8$, $QR = 17$, and $PR = 15$, let $N$ be a point on $\overline{PR}$ such that the incircles of $\triangle{PQN}$ and $\triangle{QRN}$ have equal radii. Find the ratio $\frac{PN}{RN}$ and express it as a fraction $\frac{u}{v}$, where $u$ and $v$ are relatively prime integers. Find $u + v$.

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