
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 $a\_n= \begin{cases} ( \frac {1}{3})^{n},1\leqslant n\leqslant 100 \\ \frac {2n+1}{5n-1},n > 100\end{cases}$, find $\lim\limits_{n\rightarrow\infty}a\_n$.

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