
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 $f(x)=A\cos ^{2}(ωx+φ)+1(A > 0,ω > 0,0 < φ < \dfrac {π}{2})$ with a maximum value of $3$, the coordinate of the point where the graph of the function intersects the $y$-axis is $(0,2)$, and the distance between two adjacent symmetry axes is $2$. Find the value of $f(1)+f(2)+f(3)+…+f(2016)$.

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