
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 \( f \) be a function from non-negative real numbers to non-negative real numbers, satisfying
$$
f\left(a^{3}\right)+f\left(b^{3}\right)+f\left(c^{3}\right)=3 f(a) f(b) f(c),
$$
for non-negative real numbers \( a \), \( b \), and \( c \), and \( f(1) \neq 1 \). What is \( f(2019) \)?

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