
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 $z=1+i$.
(1) Let $\omega = z^2 + 3\overline{z} - 4$, find the trigonometric form of $\omega$;
(2) If $\frac {z^{2}+az+b}{z^{2}-z+1} = 1-i$, find the values of the real numbers $a$ and $b$.

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