
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
The perimeter of triangle $XYZ$ is $130$, and the angle $XZY$ is a right angle. A circle with radius $15$ and center $O$ on $\overline{XZ}$ is drawn such that it is tangent to $\overline{XZ}$ and $\overline{ZY}$. If $OZ=\frac{a}{b}$ where $a$ and $b$ are relatively prime positive integers, find $a+b$.

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