
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 $\{a_n\}$ satisfies $\{a_n\}= \begin{cases} (\frac{1}{3}-a)n+2,n > 8 \\ a^{n-7},n\leqslant 8. \end{cases}$, find the range of the real number $a$ such that for any $n∈N^{*}$, there is $a_n > a_{n+1}$.

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