
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 general term formula of the sequence $\{a_n\}$ is $a_n=2^{5-n}$, and the general term formula of the sequence $\{b_n\}$ is $b_n=n+k$. Define the sequence $\{c_n\}$ as follows:
$$c_n = \begin{cases} b_n, & a_n \leqslant b_n \\ a_n, & a_n > b_n \end{cases}$$
If $c_5 \leqslant c_n$ holds true for any $n\in\mathbb{N}^*$, then the range of the real number $k$ is $\_\_\_\_\_\_\_\_\_\_.$

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