
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 \( f: \mathbb{R}^{+} \rightarrow \mathbb{R} \) be a continuous function satisfying \( f(xy) = f(x) + f(y) + 1 \) for all positive reals \( x, y \). If \( f(2) = 0 \), compute \( f(2015) \).

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