
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
Using Cauchy's integral formula, compute the integral

$$
\int_{C} \frac{e^{z^{2}}}{z^{2}-6 z} dz
$$

if:

1) $C:|z-2|=1$
2) $C:|z-2|=3$
3) $C:|z-2|=5$

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