
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
The cubic function \( f(x) = 4x^3 + ax^2 + bx + c \) (where \( a, b, c \in \mathbb{R} \) ) satisfies: when \( -1 \leq x \leq 1 \), \( -1 \leq f(x) \leq 1 \). Find all possible values of \( a, b, \) and \( c \).

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