
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 $f(x)= \begin{cases} a^{x}, & x < 0 \\ (a-3)x+4a, & x\geqslant 0\end{cases}$ satisfies that for any $x_{1}\neq x_{2}$, $\dfrac {f(x_{1})-f(x_{2})}{x_{2}-x_{1}} > 0$ holds, then the range of the real number $a$ is \_\_\_\_\_\_.

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