
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 the domain of the function \( f(x) \) be \( D = (-\infty, 0) \cup (0, +\infty) \), and for any \( x \in D \), it holds that \( f(x) = \frac{f(1) \cdot x^2 + f(2) \cdot x - 1}{x} \). Find the sum of all the zeros of \( f(x) \).

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