
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 the function $f(x)$ satisfies: for any real numbers $a$ and $b$, $f(a+b)=f(a)f(b)$, and $f(1)=1$, then what is the value of $\frac{f(2)}{f(1)} + \frac{f(3)}{f(2)} + \frac{f(4)}{f(3)} + \frac{f(5)}{f(4)} + \ldots + \frac{f(2011)}{f(2010)} = \_\_\_\_\_\_$.

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