
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
Consider the expression $\frac{|x^2 - |x||}{x}$. Determine for which non-zero real numbers $x$ this expression is a positive integer.
A) For positive integers $x \geq 2$ only
B) For positive integers $x \geq 1$ only
C) For all integers $x$
D) For no non-zero real numbers $x$
E) For negative integers $x$ only

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