
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 $f(x)=\begin{cases} & a^{x}(x < 0), \\\\ & (a-3)x+4a(x\geqslant 0) \\end{cases}$, which satisfies $\frac{f({x}_{1})-f({x}_{2})}{{x}_{1}-{x}_{2}} < 0$ for any ${x}_{1}\neq {x}_{2}$, find the range of values for $a$.

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