
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 circle with center \(O\) has a radius of \(10\) units and circle \(P\) has a radius of \(5\) units. The circles are externally tangent to each other at point \(Q\). Segment \(TS\) is the common external tangent to circle \(O\) and circle \(P\) at points \(T\) and \(S\), respectively. What is the length of segment \(OS\)? Express your answer in simplest radical form.

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