
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) = $\sqrt {3} \sin 2x - 2 \cos^{2} x + 1$, the horizontal coordinates of all points on the graph of f(x) are reduced to half of their original length, while the vertical coordinates remain unchanged. The resulting graph is then shifted upwards by 1 unit to obtain the graph of the function y = g(x). If g(x₁) × g(x₂) = 9, find the possible value of $|x_1 - x_2|$.

A) $\frac {\pi}{3}$
B) $\frac {\pi}{2}$
C) $\frac {3\pi}{4}$
D) $\frac {5\pi}{4}$

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