
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
In the isosceles right triangle \( \triangle ABC \), where \( \angle ABC = 90^\circ \), the coordinates of points \( A \) and \( B \) are \( A(1, 0) \) and \( B(3, 1) \), respectively. Determine the coordinates of vertex \( C \).

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