
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 $\{a_{n}\}$ is an arithmetic sequence with the first term $a$ and common difference $1$, and ${b_n}=\frac{{1+{a_n}}}{{{a_n}}}$, if $b_{n}\leqslant b_{5}$ holds for any $n\in N^{*}$, then the range of real number $a$ is ______.

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