
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
The general term of the sequence $\{a_n\}$ is given by 
$$
a_n = \begin{cases} 
2^{n}-1, & n\leq4 \\ 
-n^{2}+(a-1)n, & n\geq5
\end{cases}
$$
where $n\in\mathbb{N}^*$. If $a_5$ is the maximum value in the sequence $\{a_n\}$, then the range of values for $a$ is \_\_\_\_\_\_.

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