
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]


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Given vectors $\overrightarrow{a}=(2\cos ωx,\cos 2ωx)$ and $\overrightarrow{b}=(\sin ωx,1)$ (where $ω > 0$), let $f(x)= \overrightarrow{a}\cdot \overrightarrow{b}$ and the smallest positive period of $f(x)$ is $π$.
(1) Find the value of $f( \frac {π}{4})$;
(2) Write out the monotonically increasing interval of $f(x)$ on $\[- \frac {π}{2}, \frac {π}{2}\]$.

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