
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 complex numbers $z_1$ and $z_2$ where $|z_1| = 1 + 3i - z_1$ and $z_2 \cdot (1 - i) + (3 - 2i) = 4 + i$.  
(1) Find the complex numbers $z_1$ and $z_2$;  
(2) In the complex plane, let $O$ be the origin, and the points corresponding to complex numbers $z_1$ and $z_2$ be denoted as $A$ and $B$, respectively. Calculate the area of triangle $OAB$.

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