
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
A sphere with center $O$ has radius $9$. An isosceles triangle with sides of length $13, 13, 10$ is situated in space so that each of its sides is tangent to the sphere. Determine the distance from $O$ to the plane in which the triangle lies.

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