
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 a sequence $\left\{a_{n}\right\}$ that satisfies $a_{n}=\left\{\begin{array}{l}a^{n-2},n \lt 4\\\left(6-a\right)n-a,n\geqslant 4\end{array}\right.$, if $a_{n} \lt a_{n+1}$ holds for any $n\in N$, determine the range of real number $a$.

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