
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
Expand the function 

$$
f(z)=\frac{z}{z^{2}-2 z-3}
$$

into a Taylor series in the vicinity of the point \( z_{0}=0 \), using expansion (12), and find the radius of convergence of the series.

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