
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 $f(x)=\sin ^{2}ωx+(2 \sqrt {3}\sin ωx-\cos ωx)\cos ωx-λ$, where $ω$ and $λ$ are constants, and $ω∈( \frac {1}{2},1)$. The graph of the function is symmetric about the line $x=π$.
(1) Find the smallest positive period of function $f(x)$;
(2) If there exists $x_{0}∈[0, \frac {3π}{5}]$, such that $f(x_{0})=0$, find the range of values for $λ$.

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