
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 vectors $\overrightarrow{m}=(\cos x,1)$, $\overrightarrow{n}=(\sin x,\frac{\sqrt{3}}{2})$:

(1) When $\overrightarrow{m}$ is parallel to $\overrightarrow{n}$, find the value of $\frac{\sin x+\sqrt{3}\cos x}{\sqrt{3}\sin x-\cos x}$;

(2) In obtuse triangle $\Delta ABC$, angle $A$ is the obtuse angle, and $a,b,c$ are the sides opposite to angles $A,B,C$ respectively. If $c=2a\sin (A+B)$, and the function $f(x)={{\overrightarrow{m}}^{2}}-{{\overrightarrow{n}}^{2}}$, find the value of $f(A)$.

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