
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 $f(x)=\begin{cases} a^{x}, & x < 0 \\ (a-3)x+4a, & x\geqslant 0 \end{cases}$, it is known that for any ${x}_{1}\neq {x}_{2}$, the inequality $\frac{f({x}_{1})-f({x}_{2})}{{x}_{1}-{x}_{2}} < 0$ holds. Determine the range of values for $a$.

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