
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 $f(x)=2x^{3}-3x^{2}+cx+1$ has two extreme points $x_{1}$ and $x_{2}$ in $(0,+\infty)$, where $x_{1} < x_{2}$. The range of $\frac{f(x_{1})}{x_{2}}$ is ______.

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