
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 sector with an acute central angle $\frac{\theta}{2}$ is cut from a circle of radius 10. The radius of the circle circumscribed about the triangle formed by this sector is:
1. $5\cos\frac{\theta}{2}$
2. $5\sec\frac{\theta}{2}$
3. $5\cos\theta$
4. $5\sec\theta$
5. $5$

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