
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 general term formula of the sequence ${a_n}$: 
$$
a_n = 
\begin{cases} 
a, & n=1 \\
4n+(-1)^{n}(8-2a), & n\geq 2 
\end{cases}
$$
if for any $n\in\mathbb{N}^+$, $a_n<a_{n+1}$ always holds, then the range of values for $a$ is ______.

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