
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 radii of two concentric circles are in the ratio \( 1 : 3 \). \( AC \) is a diameter of the larger circle. \( BC \) is a chord of the larger circle and is tangent to the smaller circle. \( AB \) has length 140. What is the radius of the larger circle?

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