
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
The ratio of the radii of two concentric circles is \(1:4\). If \(\overline{AC}\) is a diameter of the larger circle, \(\overline{BC}\) is a chord of the larger circle that is tangent to the smaller circle, and \(AB=16\), find the radius of the larger circle.
A) 24
B) 28
C) 32
D) 36
E) 40

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