
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 the function $f(x)=\vec{m}\cdot\vec{n}$, where $\vec{m}=(2\cos x,1)$, $\vec{n}=(\cos x, \sqrt {3}\sin 2x)$, and $x\in R$.

1. Find the smallest positive period and the interval where the function is monotonically decreasing.
2. Find the maximum and minimum values of $f(x)$ on the interval $\left[-\frac{\pi}{6},\frac{\pi}{4}\right]$.

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