
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 $m$, $n$, $a \in \mathbb{R}$, the function $f(x) = \frac{1}{3}x^{3} - x^{2} - 3x + 2$ has a monotonically decreasing interval $A = [m, n]$ and an interval $B = [2a-3, a+3]$.

$(1)$ Find the monotonically decreasing interval $A = [m, n]$ of the function $f(x)$.

$(2)$ If "$x \in A$" is a sufficient condition for "$x \in B$", find the range of values for $a$.

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