
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 the complex number $z\_1$ that satisfies: $|z\_1|=1+3i-z\_1$. The complex number $z\_2$ satisfies: $z\_2 \cdot (1-i)+(3-2i)=4+i$.
1. Find the complex numbers $z\_1$ and $z\_2$.
2. In the complex plane, let $O$ be the origin, and let points $A$ and $B$ correspond to the complex numbers $z\_1$ and $z\_2$, respectively. Find the area of triangle $OAB$.

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