
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 that $f(x)$ is a monotonically increasing function on $\mathbb{R}$, where $f(x)$ is defined as: 
$$
f(x) =
\begin{cases}
a^x & (x > 1) \\
(4 - \frac{a}{2})x + 2 & (x \leq 1)
\end{cases}
$$
determine the range of values for the real number $a$.

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