
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 $f(x)=4x^{3}+ax^{2}bx+5$ has extreme values at $x=-1$ and $x= \dfrac {3}{2}$.

$(1)$ Write the analytical expression of the function;  
$(2)$ Determine the intervals of monotonicity of the function;  
$(3)$ Find the maximum and minimum values of $f(x)$ on the interval $[-1,2]$.

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