
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 function $f(x)=\frac{3x}{x+3}$, the general term of the sequence $\{a\_n\}$ is determined by $a\_n=f(a\_{n-1}) (n\geqslant 2$ and $n\in N^{+})$, with $a\_1=\frac{1}{2}$. Find the value of $a\_{2011}$.

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