
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 $f(x)=A\cos^2(wx+\varphi)+1$ ($A > 0$, $w > 0$, $0 < \varphi < \frac{\pi}{2}$), its maximum value is $3$, the coordinate of the intersection point of the graph of $f(x)$ with the y-axis is $(0,2)$, and the distance between two adjacent axes of symmetry is $2$. Calculate $f(1)+f(2)+f(3)+\ldots+f(2018)$.

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