
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
Find all function  $f:\mathbb{R}\rightarrow \mathbb{R}$  such that for any three real number    $a,b,c$   , if  $ a + f(b) + f(f(c)) = 0$  :  $$  f(a)^3 + bf(b)^2 + c^2f(c) = 3abc  $$  .

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