
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 functions
$$
f(x)=2x^{2}+2x-4, \quad g(x)=x^{2}-x+2,
$$

and the set \( A=\left\{ x \mid \frac{f(x)}{g(x)} \in \mathbf{Z}_{+} \right\} \).
Determine the set \( A \).

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