
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
Given the sequence $\{a_n\}$ with the general term formula $a_n= \begin{cases} \frac {1}{n}, & n=1,2 \\ ( \frac {1}{2})^{n}, & n\geqslant 3\end{cases}$, where $n\in\mathbb{N}^*$, and its sum of the first $n$ terms is $S_n$, then $\lim_{n\rightarrow \infty}S_n=$ ______.

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