
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 $f(x)=2\sin ^{2}(ωx+ \frac {π}{4})+2\cos ^{2}ωx(ω > 0)$, where the distance between two adjacent lowest points on its graph is $\frac {2π}{3}$.
(1) Find the maximum value of the function $f(x)$ and the corresponding value of $x$.
(2) If the graph of function $g(x)$ is obtained by shifting the graph of $f(x)$ to the right by $\frac {π}{8}$ units and then reflecting it about the $y$-axis, find the interval(s) where $g(x)$ is decreasing.

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