
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 $\vec{a}=(-2\sin x, -1)$ and $\vec{b}=(-\cos x, \cos 2x)$, define the function $f(x)=\vec{a}\cdot\vec{b}$.
(1) Find the expression for the function $f(x)$, and identify its maximum and minimum values;
(2) In an acute-angled triangle $\triangle ABC$, with angles $A$, $B$, $C$ opposite to sides $a$, $b$, $c$ respectively, and $f(A)=1$, $bc=8$, find the area $S$ of $\triangle ABC$.

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