
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
Given a function $f(x) = \frac{1}{3}x^{3} + ax + b$ ($a, b \in \mathbb{R}$), it has a minimum value of $-\frac{4}{3}$ at $x = 2$.  
(1) Find $f(x)$.  
(2) If $\frac{1}{3}x^{3} + ax + b \leq m^{2} + m + \frac{10}{3}$ holds true for all $x \in [-4, 3]$, determine the range of values for $m$.

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