
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 $f(x)= \begin{cases} -x^{2}+(2a-2)x,x\leqslant 0 \\ x^{3}-(3a+3)x^{2}+ax,x > 0\\ \end{cases}$, if the tangent lines at points $P_{i}(x_{i},f(x_{i}))(i=1,2,3)$, where $x_{1}$, $x_{2}$, $x_{3}$ are distinct, on the curve $y=f(x)$ are parallel to each other, then the range of values for $a$ is $\_\_\_\_\_\_$.

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