
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 $f(x)=x\ln x-x+ \frac {1}{2}x^{2}- \frac {1}{3}ax^{3}$, let the derivative of $f(x)$ be $y=g(x)$.
$(I)$ Determine the monotonicity of $y=g(x)$ within its domain;
$(II)$ If there exist two tangent lines on the curve $y=f(x)$ that have acute angles and are parallel to each other, find the range of the real number $a$.

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