
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 a function $y=f(x)$ on $\mathbb{R}$, which has the following properties:  
① For any $x \in \mathbb{R}$, $f(x^3) = [f(x)]^3$; ② For any $x_1, x_2 \in \mathbb{R}$, if $x_1 \neq x_2$, then $f(x_1) \neq f(x_2)$.  
Find the value of $f(0) + f(-1) + f(1)$.

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