
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 $f(x) = e^{|x|} - \frac{1}{x^2 + 2}$, determine the range of $x$ values that satisfy $f(x) > f(2x - 1)$.

A) $\left(\frac{1}{3}, 1\right)$
B) $\left(-\infty, \frac{1}{3}\right) \cup \left(1, +\infty\right)$
C) $\left(-\frac{1}{3}, \frac{1}{3}\right)$
D) $\left(-\infty, -\frac{1}{3}\right) \cup \left(\frac{1}{3}, +\infty\right)$

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