
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 $f(x)=A\cos^2(ωx+φ)+1$ where $A > 0$, $ω > 0$, and $0 < φ < \dfrac {π}{2}$, the maximum value of the function is $3$, and the point on the graph of $f(x)$ symmetric about the $y$-axis has coordinates $( ,2)$. The distance between two adjacent symmetrical points is $2$. Find the value of $f(1)+f(2)+...+f(26)$.

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