
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 $\vec{a}=(2\sin x,\sqrt{3}\cos x)$, $\vec{b}=(\cos x,2\cos x)$, and the function $f\left( x \right)=\vec{a}\cdot \vec{b}-\sqrt{3}$,

(Ⅰ) Find the smallest positive period of the function $f\left( x \right)$;

(Ⅱ) Find the intervals where the function $f\left( x \right)$ is monotonically decreasing.

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