
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 \( f \) is such that for any positive \( x \) and \( y \) it satisfies the equation \( f(xy) = f(x) + f(y) \). Find \( f(2007) \) if \( f\left(\frac{1007}{1024}\right) = 1 \).

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