
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 a function $f(x)=2\sin (\omega x+\varphi)+2$ ($\omega > 0$, $|\varphi| < \frac{\pi}{2}$) with the smallest positive period of $2$, and its graph passes through the point $(0,3)$, and one of the symmetry centers of the graph of $f(x)$ is $(a,b)$, then the minimum value of $|a+b|$ is ______.

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