
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
Determine the locus of point \( C \) under the following conditions: Given an angle \(\widehat{ASB}\), construct two circles, one of which is tangent to the ray \(SA\) at point \(A\) and the other to the ray \(SB\) at point \(B\). The two circles are tangent to each other at point \(C\). What is the locus of point \(C\)?

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