
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
Define the function \( y = f(x) \) on \(\mathbf{R}\), which has the following properties:
(1) For any \( x \in \mathbf{R} \), \( f\left(x^{3}\right) = f^{3}(x) \);
(2) For any \( x_{1}, x_{2} \in \mathbf{R}, x_{1} \neq x_{2} \), \( f\left(x_{1}\right) \neq f\left(x_{2}\right) \). Find the value of \( f(0) + f(1) + f(-1) \).

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