
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 $f(x) = \begin{cases} (a- \frac {1}{2})x, & x\geq2 \\ a^{x}-4, & x<2\end{cases}$, it satisfies that for any real numbers $x_1 \neq x_2$, the inequality $\frac {f(x_{1})-f(x_{2})}{x_{1}-x_{2}} > 0$ holds. Determine the range of the real number $a$.

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