
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
**(This question is worth 12 points)** Given points A(1,1), B(3, -1), and C(a, b).  
(1) If points A, B, and C are collinear, find the relationship between a and b.  
(2) If $\overrightarrow{AC} = 2$, find the coordinates of point C.

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