
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
Suppose the function $f(x) = x(\ln x - 2ax)$ (where $a$ is a constant) has two extreme points ${x_1}, {x_2}$ (${x_1} < {x_2}$), determine the relationship between $f({x_1})$ and $f({x_2})$.

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