
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
The sum of the first n terms of an infinite geometric sequence $\{a_n\}$ (where $n \in \mathbb{N}^*$) is $S_n$, and $$\lim_{n \to \infty}S_{n}= \frac {1}{2}$$, then the range of the first term $a_1$ is \_\_\_\_\_\_.

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