
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
Inside an angle, there are three circles $\mathrm{S}_{1}, \mathrm{~S}_{2}, \mathrm{~S}_{3}$, each of which is tangent to the two sides of the angle. The circle $S_{2}$ is externally tangent to the circles $S_{1}$ and $S_{3}$. It is known that the radius of circle $S_{1}$ is 1, and the radius of circle $S_{3}$ is 9. What is the radius of circle $S_{2}$?

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