
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 $f(x)=2\cos ^{2}ωx-1+2 \sqrt{3}\cos ωx\sin ωx(0 < ω < 1)$, the line $x= \frac{π}{3}$ is a symmetry axis of the graph of $f(x)$.

(1) Find the value of $ω$; and discuss the monotonicity of the function in $\[- \frac{π}{2}, \frac{π}{2}\]$;

(2) Given that the graph of the function $y=g(x)$ is obtained by stretching the horizontal coordinates of each point of the graph of $y=f(x)$ to twice the original, then moving it to the left by $ \frac{2π}{3}$ units. If $g(2α + \frac{π}{3})= \frac{8}{5}$, $α ∈ (0, \frac{π}{2})$, find the value of $\sin α$.

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