
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 $190$, and the angle $BAC$ is a right angle. A circle with radius $23$ and center $O$ on $\overline{AB}$ is drawn so that it is tangent to $\overline{BC}$. Find the exact length of $\overline{AO}$ if $AO=x/y$ where $x$ and $y$ are relatively prime positive integers, then provide the value of $x+y$.

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