
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 function $f(x)=a\ln x+ \frac {1}{2}x^{2}$, for any two distinct real numbers $x_{1}$, $x_{2}$ within its domain, the inequality $\frac {f(x_{1}+a)-f(x_{2}+a)}{x_{1}-x_{2}}\geqslant 3$ always holds. Then, the range of the real number $a$ is \_\_\_\_\_\_.

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