
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 $f(x) = a\ln x+ \frac{1}{2}x^2-ax$ (where $a$ is a constant), it has two extreme points.  
(1) Determine the range of values for the real number $a$.  
(2) Suppose the two extreme points of $f(x)$ are $x_1$ and $x_2$, if the inequality $f(x_1) + f(x_2) < \lambda(x_1 + x_2)$ holds true for any values of $x_1$ and $x_2$, find the minimum value of $\lambda$.

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