
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 $\{a_n\}$ satisfying 
$$
a_n= 
\begin{cases} 
(1-3a)n + 10a & ,n \leq 6 \\
a^{n-7} & ,n>6 
\end{cases}
$$
where $n\in\mathbb{N}^*$, if $\{a_n\}$ is a decreasing sequence, then the range of the real number $a$ is ______.

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