
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 \( f: \mathbf{R} \rightarrow \mathbf{R} \) satisfy the functional equation
$$
f\left(x^{3}\right)+f\left(y^{3}\right)=(x+y) f\left(x^{2}\right)+f\left(y^{2}\right)-f(x y).
$$

Find the explicit form of the function \( f(x) \).
(2012, Albania Mathematical Olympiad)

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