
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 $f(x)=\begin{cases} a^{x-5}, & x\geqslant 6, \\ (4-\frac{a}{2})x+4, & x < 6, \end{cases}$ and the sequence $\{a_n\}$ satisfies $a_n=f(n) (n\in \mathbb{N}^*)$, and the sequence $\{a_n\}$ is increasing, then the range of the real number $a$ is ______.

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