
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 function defined on the set of real numbers, \(f(x)\), satisfies \(f(x-1) = \frac{1 + f(x+1)}{1 - f(x+1)}\). Find the value of \(f(1) \cdot f(2) \cdot f(3) \cdots f(2008) + 2008\).

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