
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 $f(x)=\begin{cases}(3a-1)x+4a, & x < 1 \\ \log_{a}x, & x\geqslant 1\end{cases}$ satisfies: for any real numbers $x_{1}$, $x_{2}$, when $x_{1} < x_{2}$, it always holds that $f(x_{1})-f(x_{2}) > 0$, determine the range of the real number $a$.

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