
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 sequence $\{a_n\}$ with the general term $a_n= \begin{cases} n+ \frac {15}{n}, & n\leqslant 5 \\ a\ln n- \frac {1}{4}, & n > 5\end{cases}$, if the minimum value of $\{a_n\}$ 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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