
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 $f(x) = \frac{1+x}{1-x}$, and let $f\_1(x) = f(x)$, $f_{k+1}(x) = f(f_k(x))$, $k = 1, 2, ...$, find an expression for $f_{2010}(x)$.

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