
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 $\overrightarrow{a}=(\cos ωx,\sin ωx)$ and $\overrightarrow{b}=(\cos ωx, \sqrt {3}\cos ωx)$, where $ω > 0$, define the function $f(x)= \overrightarrow{a} \cdot \overrightarrow{b}$.
(1) If the smallest positive period of the function $f(x)$ is $π$, find the interval where the function $f(x)$ is monotonically increasing.
(2) If the horizontal coordinate of a symmetry center of the graph of the function $f(x)$ is $\frac {π}{6}$, find the minimum value of $ω$.

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