
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 vectors $\overrightarrow{a}=(\cos ωx-\sin ωx,\sin ωx)$ and $\overrightarrow{b}=(-\cos ωx-\sin ωx,2 \sqrt {3}\cos ωx)$, and a function $f(x)= \overrightarrow{a} \cdot \overrightarrow{b}+λ(x\in R)$ whose graph is symmetrical about the line $x=π$, where $ω$ and $λ$ are constants, and $ω\in( \frac {1}{2},1)$.

1. Find the smallest positive period of the function $f(x)$;
2. If the graph of $y=f(x)$ passes through the point $(\frac{π}{4},0)$, find the range of the function $f(x)$ in the interval $[0, \frac{3π}{5}]$.

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