
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 $ABC$ is $198$, and the angle $BAC$ is a right angle. A circle of radius $22$ with center $O$ on $\overline{AB}$ is drawn so that it is tangent to $\overline{AC}$ and $\overline{BC}$. Given that $OB=d/e$ where $d$ and $e$ are relatively prime positive integers, find $d+e$.

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