
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 $f(x)=\begin{cases}
(3a-2)x+6a-1 & (x < 1) \\
a^{x} & (x\geqslant 1)
\end{cases}$ is monotonically decreasing on $\mathbb{R}$, find the range of real number $a$.

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