
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 that the general term of the sequence $\{a_{n}\}$ is $a_{n}=2^{5-n}$, and the general term of the sequence $\{b_{n}\}$ is $b_{n}=n+k$. Let $c_{n}=\left\{\begin{array}{l}{b_n},{a_n}≤{b_n}\\{a_n},{a_n}>{b_n}\end{array}\right.$. If $c_{5}\leqslant c_{n}$ holds for any $n\in N^{*}$ in the sequence $\{c_{n}\}$, then the range of real number $k$ is ____.

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