
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 $f(x) = x^2 - 2x + a \ln x$ with two extreme points $(x_1, x_2)$, where $x_1 < x_2$, determine the range of values for $f(x_2)$.
A) $(-1, \frac{-3 + 2\ln 2}{4})$
B) $(-\infty, \frac{-3 - 2\ln 2}{4})$
C) $(\frac{-3 + 2\ln 2}{4}, +\infty)$
D) $(\frac{-3 - 2\ln 2}{4}, -1)$

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