
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 an isosceles right triangle \( A B S \) with base \( A B \). On the circle centered at point \( S \) that passes through points \( A \) and \( B \), there is a point \( C \) such that triangle \( A B C \) is isosceles.

Determine how many points \( C \) satisfy the given conditions, and construct all such points.

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