
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 $$f(x)=\sin^{2}\omega x+2 \sqrt {3}\sin\omega x\cdot \cos\omega x-\cos^{2}\omega x+\lambda (\lambda\in\mathbb{R})$$ is symmetric about the line $$x= \frac {\pi}{3}$$, where $\omega$ and $\lambda$ are constants and $\omega\in(0,2)$.  
(1) Find the smallest positive period of the function $f(x)$.  
(2) If the graph of $y=f(x)$ passes through the point $$( \frac {\pi}{6},0)$$, find the range of the function $f(x)$ on $$x\in[0, \frac {\pi}{2}]$$.

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