
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 \( f(3) \) for the function \( f : \mathbb{R} \to \mathbb{R} \) satisfying
\[ f(x) + 3f(1 - x) = 4x^3 \] for all \( x \).

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