
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 $\overset{→}{a}=(\sqrt{3}\sin x,\sin x)$, $\overset{→}{b}=(\cos x,\sin x)$, where $x\in[0,\frac{\pi}{2}]$,

(1) Find the value of $x$ if $|\overset{→}{a}|=|\overset{→}{b}|$;

(2) Let $f(x)=\overset{→}{a}\cdot\overset{→}{b}$, find the maximum value of $f(x)$.

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