
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 number $z=(1+i)^{2}+\frac{2i}{1+i}$, where $i$ is the imaginary unit.<br/>$(1)$ Find $z$ and $|z|$;<br/>$(2)$ If $z^{2}+a\overline{z}+b=2+3i$, find the values of real numbers $a$ and $b$.

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