
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
Suppose the domain of function $y=f(x)$ is $D$. If for any $x_{1}, x_{2} \in D$, when $x_{1} + x_{2} = 2a$, it always holds that $f(x_{1}) + f(x_{2}) = 2b$, then the point $(a,b)$ is called the center of symmetry of the graph of the function $y=f(x)$. Investigate a center of symmetry for the function $f(x) = 2x + 3\cos\left(\frac{\pi}{2}x\right) - 3$ and use the definition of the center of symmetry to find the value of $f\left(\frac{1}{2018}\right) + f\left(\frac{2}{2018}\right) + \ldots + f\left(\frac{4034}{2018}\right) + f\left(\frac{4035}{2018}\right)$.

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