
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 $f(x)=\sin x-2 \sqrt{3}\sin ^{2} \frac{x}{2}$.

(1) Find the smallest positive period and the monotonically decreasing interval of $f(x)$;

(2) Find the minimum value of $f(x)$ on the interval $\left[\begin{matrix}\begin{matrix}0, \frac{2\pi}{3} \end{matrix}\end{matrix}\right]$.

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