
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: $x^2+y^2=1$ (1); $x^2+(y-3)^2=1$ (2). By subtracting equation (2) from equation (1), we can obtain the equation of the axis of symmetry of the two aforementioned circles. Generalize the proposition under the condition that the curve remains a circle. That is, find a more general proposition where the known proposition should be a special case of the generalized proposition. The generalized proposition is ____.

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