
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 of the sequence $\left\{a_{n}\right\}$ as ${a_{n}}=\begin{cases} n+\frac{15}{n},n\leqslant 5 \\ a\ln n-\frac{1}{4},n > 5 \end{cases}$, if the minimum value of $\left\{a_{n}\right\}$ is $\frac{31}{4}$, then the range of the real number $a$ is ________.

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