
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 following functions into Taylor series (using known expansions) and find the radii of convergence:

a) $\sin (3z + 2)$ in powers of $z + 1$;

b) $e^z$ in powers of $2z + 1$;

c) $\frac{z+1}{z^2 - 3z + 2}$ in powers of $z$;

d) $\ln (3 - z)$ in powers of $z$.

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