
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 the function $f(x)$ satisfy the condition that for any $m, n \in \mathbb{Z}_+$, $f(m + n) = f(m) \cdot f(n)$ and $f(1) = 2$. Calculate $\frac{f(2)}{f(1)} + \frac{f(3)}{f(2)} + \ldots + \frac{f(2011)}{f(2010)}$.

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