
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
Given two circles \( x^{2}+y^{2}-2 a x=0 \) and \( x^{2}+y^{2}-2 b y=0 \), where \( b \neq 0 \), find the equation of the circle whose diameter is the common chord of the given circles.

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