
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
Two circles with radii 12 cm and 15 cm overlap such that the distance between their centers is 20 cm. Determine the length of the common chord of the two circles.

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