
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 that \( f(a+b) = f(a) \cdot f(b) \) and \( f(1) = 1 \), find the value of the expression \(\frac{f(2)}{f(1)}+\frac{f(3)}{f(2)}+\cdots+\frac{f(2005)}{f(2004)}\).

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