
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 of numbers \( t_{1}, t_{2}, t_{3}, \ldots \) is defined by

$$
\left\{
\begin{array}{l}
t_{1}=2 \\
t_{n+1}=\frac{t_{n}-1}{t_{n}+1}
\end{array}
\right.
$$

for each positive integer \( n \). Find \( t_{2011} \).

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