
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 = $$\frac{(1+i)^{2}+3(1−i)}{2+i}$$ (where i is the imaginary unit), find:
1. The modulus of z, denoted as |z|.
2. If z^2 + az + b = 1 + i (where a, b are real numbers), find the value of a + b.

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