
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(x)cos(x) - cos^2(x) - $\frac{1}{2}$.
(I) Find the equation of the symmetry axis of the function f(x).
(II) Stretch the horizontal coordinates of the graph of function f(x) by a factor of 2 while keeping the vertical coordinates unchanged, then shift it to the left by $\frac{\pi}{3}$ units to obtain the graph of function g(x). If a, b, and c are the lengths of the sides opposite to angles A, B, and C of △ABC respectively, with a = 2, c = 4, and g(B) = 0, find the value of b.

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