
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
The function $f(x)=\begin{cases}|\log_{3}x|, & 0 < x < 3 \\ \frac{1}{3}x^{2}- \frac{10}{3}x+8, & x\geqslant 3\end{cases}$, if there exist $a,b,c,d\in\mathbb{R}$, satisfying $f(a)=f(b)=f(c)=f(d)$, where $d > c > b > a > 0$, then the range of $2a+b+c+d$ is \_\_\_\_\_\_.

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