
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 $f(x)=\sin (ωx+φ)(ω > 0,0≤φ≤π)$, it is an even function, and the distance between two adjacent lowest points on its graph is $2π$.
(I) Find the analytic expression of $f(x)$;
(II) If the graph of function $f(x)$ is shifted to the right by $\frac {π}{3}$ units to obtain the graph of function $g(x)$, and $α∈[0,π]$, such that $g(α)= \frac {1}{2}$, find the value of $α$.

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