
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 general term formula of the sequence $\{a_n\}$ is 
$$
a_n = \begin{cases} 
\left( \frac {1}{3} \right)^{n}, & 1 \leq n \leq 100 \\ 
\frac {2n+1}{5n-1}, & n > 100
\end{cases}
$$
Then, $\lim_{n \to \infty} a_n = \_\_\_\_\_\_$.

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