
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
Point \( A \) lies on the circumference of the upper base of a right circular cylinder, \( B \) is the farthest point from it on the circumference of the lower base, and \( C \) is an arbitrary point on the circumference of the lower base. Find \( AB \) if \( AC = 12 \) and \( BC = 5 \).

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