
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 sequence $\{a_n\}$ is a geometric sequence, and the sum of the first $n$ terms is $S_n$. If $a_1 + a_2 = 2$ and $a_2 + a_3 = -1$, then the limit $\lim_{n \rightarrow \infty} S_n = \_\_\_\_\_$.

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