
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 $f(x)=x^{3}+(4-a)x^{2}-15x+a$, where $a\in \mathbb{R}$.
- $(I)$ If point $P(0,-2)$ is on the graph of the function $f(x)$, find the value of $a$ and the minimum value of the function $f(x)$;
- $(II)$ If the function $f(x)$ is monotonically decreasing on the interval $(-1,1)$, find the maximum value of $a$.

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