
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 $g(x)=ax^{3}+bx^{2}+cx+d(a\neq 0)$, its derivative is $f(x)$, $a+b+c=0$, and $f(0)⋅f(1) > 0$. Let $x\_{1}$, $x\_{2}$ be the two roots of the equation $f(x)=0$. Determine the range of $|x\_{1}-x\_{2}|$.

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