
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
For the sequence $\{a_{n}\}$, define ${A_n}=\frac{{{a_1}+2{a_2}+…+{2^{n-1}}{a_n}}}{n}$ as the "good number" of the sequence $\{a_{n}\}$. Given that the "good number" of a certain sequence $\{a_{n}\}$ is ${A_n}={2^{n+1}}$, and the sum of the first $n$ terms of the sequence $\{a_{n}-kn\}$ is denoted as $S_{n}$, if $S_{n}\leqslant S_{6}$ holds for any $n\in N^{*}$, then the range of real number $k$ is ____.

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