
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
Let there be two circles, \(K_1\) and \(K_2\), with centers \(F_1\) and \(F_2\). Denote the distance of an arbitrary point from the two circles as \(d_1\) and \(d_2\), respectively.

What is the locus of points for which the ratio \(d_1 : d_2\) is constant?

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