
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 $f(x)=\sqrt{3}\sin x\cos x-\cos ^{2}x-\dfrac{1}{2}$.
(I) Find the equation of the symmetry axis of the function $f(x)$;
(II) Stretch the horizontal coordinates of each point on the graph of the function $f(x)$ by a factor of 2 while keeping the vertical coordinates unchanged, then shift the resulting graph to the left by $\dfrac{\pi }{3}$ units to obtain the graph of the function $g(x)$. If $a$, $b$, $c$ are the lengths of the sides opposite to angles $A$, $B$, $C$ of $\triangle ABC$ 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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