
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 $f(x) = \begin{cases} a^{x},x < 0 \\ (a-4)x+3a,x\geqslant 0\end{cases}$, find the range of $a$ that satisfies $[f(x_{1})-f(x_{2})](x_{1}-x_{2}) < 0$ for any two different $x_{1}$, $x_{2}$ in the domain.

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