
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
In a circle with a radius of 5, a chord \( AB = 8 \) is drawn. Point \( C \) lies on the chord \( AB \) such that \( AC:BC = 1:2 \). Find the radius of a circle that is tangent to the given circle and tangent to the chord \( AB \) at point \( C \).

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