
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 side lengths $PQ = 15$, $PR = 8$, and $QR = 17$, let $O$ and $I$ denote the circumcenter and incenter, respectively. A circle with center $N$ is tangent to the legs $PR$ and $QR$ and to the circumcircle of $\triangle{PQR}$. What is the area of $\triangle{NOI}$?

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