
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 numbers $z\_1=(1+bi)(2+i)$ and $z\_2=3+(1-a)i$, where $a,b \in \mathbb{R}$ and $i$ is the imaginary unit.

1. Find the values of the real numbers $a$ and $b$ if $z\_1=z\_2$.
2. If $b=1$ and $a=0$, find $| \frac{z\_1+\overline{z\_2}}{1-2i} |$.

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