
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 $f(x)= \begin{cases} (3a-1)x+4a,x < 1 \\ \log _{a}x,x\geqslant 1 \end{cases}$ that satisfies: for any real numbers $x_{1}$, $x_{2}$, when $x_{1} < x_{2}$, there is always $f(x_{1})-f(x_{2}) > 0$. Determine the range of values for the real number $a$.

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