
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
Find the limits of the functions:
a) \(\lim _{z \rightarrow 1-i} \frac{z^{2}-2 z+2}{z-1+i}\);

b) \(\lim _{z \rightarrow 0} \frac{1}{z}\left\{\sqrt{z+i}-\frac{1}{\sqrt{2}}(1+i)\right\}\);

c) \(\lim _{z \rightarrow 0} \frac{\sin 3 z}{z}\);

d) \(\lim _{z \rightarrow z_{0}} \frac{\ln z-\ln z_{0}}{z-z_{0}}, \quad z_{0} \neq 0+0i\).

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