
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 $8$ units, and a circle $P$ with center $C$ has a radius of $4$ units. Both circles are externally tangent to each other at point $Q$. Another circle, also centered at point $C$ and also with a radius of $4$ units, is externally tangent to circle $P$. Segments $TS$ is the common external tangent of circle $O$ and circle $C$ 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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