
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 $\overrightarrow{a}=(\cos x,\sin x)$ and $\overrightarrow{b}=(3,-\sqrt{3})$, where $x\in [0,\pi]$.

(1) Find the value of $x$ when $\overrightarrow{a}$ is parallel to $\overrightarrow{b}$;

(2) Let $f(x)=\overrightarrow{a}\cdot \overrightarrow{b}$. Find the maximum and minimum values of $f(x)$ and their corresponding $x$ values.

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