
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 $\{a\_n\}$ that satisfies $a\_n= \begin{cases} (\frac{1}{2}-a)n+1 & (n < 6) \\ a^{n-5} & (n\geqslant 6) \end{cases}$, if $a\_n > a\_{n+1}$ holds true for any $n∈N^{*}$, find the range of the real number $a$.

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