
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 $PQR$ is a right triangle with $PQ = 8$, $QR = 15$, and the right angle at $R$. Point $N$ is the midpoint of $PR$, and $E$ is on the same side of line $PR$ as $Q$ such that $PE = NE = 17$. Given that the area of triangle $REN$ may be expressed as $\frac {x\sqrt {y}}{z}$, where $x$, $y$, and $z$ are positive integers, $x$ and $z$ are relatively prime, and $y$ is not divisible by the square of any prime, find $x + y + z$.

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