
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 $f(x) = \begin{cases} (3a-1)x+4a & (x < 1) \\ \log_{a}x & (x \geq 1)\end{cases}$ is not a monotonic function on $\mathbb{R}$, then the range of real number $a$ is \_\_\_\_\_\_

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