
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 $f(x)=4\sin (ωx- \frac {π}{4})⋅\cos ωx$ reaches its extreme value at $x= \frac {π}{4}$, where $ω∈(0,2)$.
(1) Find the minimum positive period of the function $f(x)$;
(2) Translate the graph of the function $f(x)$ to the left by $\frac {π}{36}$ units, then stretch the abscissa of each point on the obtained graph to three times the original, and the ordinate remains unchanged to obtain the graph of the function $y=g(x)$. If $α$ is an acute angle and $g(α)= \frac {4}{3}- \sqrt {2}$, find $\cos α$.

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