
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 sequence $\{a_n\}$ satisfying 
$$
a_n= 
\begin{cases} 
(5-a)n-11, & \text{if } n \leq 5, \\
a^{n-4}, & \text{if } n > 5,
\end{cases}
$$
and $\{a_n\}$ is an increasing sequence, determine the range of the real number $a$.

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