
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
Let \( f(x) = \frac{x-1}{x+1} \), and define \( f_{n}(x) = \underbrace{f\{f[f \cdots f}_{n \uparrow f}(x)]\} \). Find the general expression for \( f_{1999}(x) \).

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