
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
If $f(a+b) = f(a) \cdot f(b)$ for any $a, b \in \mathbb{N^{*}}$, and $f(1) = 2$, compute the value of 
$$\frac{f(2)}{f(1)} + \frac{f(4)}{f(3)} + \ldots + \frac{f(2012)}{f(2011)}.$$

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