
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 $f(x)=A\sin ^{2}(ωx+φ)$ $(A > 0,ω > 0,0 < φ < \dfrac {π }{2})$, the maximum value of $y=f(x)$ is $2$, the distance between the adjacent symmetry axes of the graph is $2$, and it passes through the point $(1,2)$.
(I) Find $ϕ$;
(II) Calculate $f(1)+f(2)+…+f(2008)$.

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