
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
Draw a line through the intersection point of two circles such that the circles cut chords on this line, with the sum of the chord lengths being the largest possible. (The centers of the circles are located on opposite sides of their common chord).

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