
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
In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and they satisfy $\left( {{a}^{{2}}}+{{c}^{{2}}}-{{b}^{{2}}} \right){\tan }B=\sqrt{3}\left( {{b}^{{2}}}+{{c}^{{2}}}-{{a}^{{2}}} \right)$.

(1) Find angle $A$;

(2) If the area of $\triangle ABC$ is $\dfrac{3}{2}$, find the value of $\dfrac{(bc-4\sqrt{3})\cos A+ac\cos B}{{{a}^{2}}-{{b}^{2}}}$.

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