
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 $a\_n= \begin{cases} (1-3a)n+10a,n\leqslant 6 \\ a^{n-7},n > 6\end{cases} (n\in\mathbb{N}^*)$, if $\{a\_n\}$ is a decreasing sequence, determine the range of the real number $a$.

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