
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 the function $f(x)= \frac {1}{3}ax^{3}+ \frac {1}{2}(a+1)x^{2}-(a+2)x+6$, where $a\in\mathbb{R}$.  
$(1)$ If $f(x)$ has a maximum value at $x=-3$, does it have a minimum value? If it exists, find the minimum value. If not, explain why;  
$(2)$ If the function $f(x)$ is monotonic on $\mathbb{R}$, find the range of values for $a$.

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