
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 interval of convergence of the power series

$$
1-\frac{x}{2 \cdot 2}+\frac{x^{2}}{3 \cdot 2^{2}}-\frac{x^{3}}{4 \cdot 2^{3}}+\ldots+(-1)^{n} \frac{x^{n}}{(n+1) 2^{n}}+\ldots
$$

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