
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
Let vectors $\overrightarrow{a}=( \sqrt{3}\sin x,\sin x )$ and $\overrightarrow{b}=( \cos x,\sin x )$, where $x\in \left[ 0,\frac{\pi }{2} \right]$.

(1) If $|\overrightarrow{a}|=|\overrightarrow{b}|$, find the value of $x$;

(2) Let the function $f\left( x \right)=\overrightarrow{a}\cdot \overrightarrow{b}$, find the maximum and minimum values of $f\left( x \right)$.

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