
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 a function $f\left(x\right)=\left\{\begin{array}{l}{(a-3)x+5, x\leq 1}\\{\frac{3a}{x}, x>1}\end{array}\right.$, if for any real numbers $x_{1}$ and $x_{2}$ in $\mathbb{R}$, where $x_{1} \neq x_{2}$, the inequality $(x_{1}-x_{2})[f(x_{1})-f(x_{2})] \lt 0$ always holds, then the range of values for $a$ is ______.

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