
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
Let $f(x)=\left\{\begin{array}{l}(2a-1)x+4a & (x<1)\\ \frac{a}{x} & (x\geq 1)\end{array}\right.$, for $\forall x_{1}, x_{2} \in \mathbb{R}$, $x_{1} \neq x_{2}$, if $\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} < 0$ holds, then the range of $a$ is ______.

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