
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 $f(x)=\sin^2x-\cos^2x+2\sqrt{3}\sin x \cos x+\lambda (x\in \mathbb{R})$, where $\lambda$ is a real constant. <br/>$(1)$ Find the smallest positive period of the function $y=f(x)$; <br/>$(2)$ If the graph of the function $y=f(x)$ passes through the point $(\frac{\pi}{2},0)$, find the maximum and minimum values of the function on the interval $[0,\frac{2}{3}\pi]$.

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