
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 $f\left(x\right)=x^{3}-3x^{2}+ax+b$ has a tangent line parallel to the $x$-axis at $x=-1$. Find:<br/>
$(1)$ the value of $a$ and the intervals where the function $f\left(x\right)$ is monotonic;<br/>
$(2)$ if the graph of the function $y=f\left(x\right)$ has exactly three distinct intersection points with the parabola $y=\frac{3}{2}x^{2}-15x+3$, find the range of values for $b$.

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