
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]


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Given the vectors $\overrightarrow{m} = (\cos x, -1)$ and $\overrightarrow{n} = (\sqrt{3}\sin x, -\frac{1}{2})$.
(1) When $\overrightarrow{m} \parallel \overrightarrow{n}$, find the value of $\frac{\sqrt{3}\sin x + \cos x}{\sin x - \sqrt{3}\cos x}$;
(2) Given that in an acute-angled triangle $ABC$, $a$, $b$, and $c$ are the sides opposite angles $A$, $B$, and $C$ respectively, and $\sqrt{3}c = 2a\sin(A + B)$, let the function $f(x) = (\overrightarrow{m} + \overrightarrow{n}) \cdot \overrightarrow{m}$. Find the range of values for $f(B)$.

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