
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)** **In the complex plane, points A, B, C correspond to the complex numbers 1, 2 + i, -1 + 2i, respectively.**  
**(1) Find the complex numbers corresponding to , , ;**  
**(2) Determine the shape of triangle ABC;**  
**(3) Calculate the area of triangle ABC.**

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