
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 $f(x)=\sqrt{3}\sin(ωx+φ)-\cos(ωx+φ)$ $(0 < φ < π, ω > 0)$ is an even function, and the distance between two adjacent symmetry axes of the graph of $y=f(x)$ is $\frac{π}{2}$.

(1) Find the value of $f(\frac{π}{8})$;

(2) After translating the graph of $y=f(x)$ to the right by $\frac{π}{6}$ units, then stretching the $x$-coordinate of each point on the resulting graph to four times its original length (while keeping the $y$-coordinate unchanged) to obtain the graph of $y=g(x)$, find the interval(s) on which $g(x)$ is decreasing.

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