
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 the domain of the function $f(x)$ is $(-\infty, 0) \cup (0, +\infty)$, for any $x_1, x_2$ within the domain, it holds that $f(x_1 \cdot x_2) = f(x_1) + f(x_2)$. Find the value of $f(1)$.

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