
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 $\overrightarrow{m}=(\cos ωx, \sqrt {3}\cos (ωx+π))$ and $\overrightarrow{n}=(\sin ωx,\cos ωx)$, where $ω > 0$, and $f(x)= \overrightarrow{m} \cdot \overrightarrow{n}$. The distance between adjacent symmetry axes of $f(x)$ is $\frac {π}{2}$.
(I) If $f(\frac {α}{2})=- \frac {\sqrt {3}}{4}$, where $α \in (0, \frac {π}{2})$, find the value of $\cos α$.
(II) The horizontal coordinates of each point on the graph of $y=f(x)$ are stretched to twice their original length, while the vertical coordinates remain unchanged. Then, the graph is shifted to the left by $\frac {π}{6}$ units to obtain the graph of $y=g(x)$. Find the interval where $y=g(x)$ is monotonically increasing.

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