
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 ${a_n}$, define its "good number" ${A_n}=\frac{a_1+2a_2+...+2^{n-1}a_n}{n}$. It is known that the "good number" of a certain sequence ${a_n}$ is ${A_n=2^{n+1}}$. Let ${S_n}$ denote the sum of the first $n$ terms of the sequence ${a_n-kn}$. If ${S_n \leq S_6}$ holds for any $n\in N^*$, determine the range of the real number $k$.

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