
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 \( f(x)=\begin{cases} -x+3a, & x < 0 \\ a^{x}, & x\geqslant 0 \end{cases} (a > 0, a\ne 1) \), and in the domain \( \mathbb{R} \) it satisfies \( \dfrac{f(x_1)-f(x_2)}{x_1-x_2} < 0 \), determine the range of \( a \).

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