
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 the function $f(x) = ax^3 - bx + 4$ ($a, b \in \mathbb{R}$). When $x=2$, the function $f(x)$ has an extremum of $- \frac{4}{3}$.  
(1) Find the explicit formula of the function $f(x)$.  
(2) If the equation $f(x) = k$ has 3 distinct roots, find the range of the real number $k$.

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