
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
In a Cartesian coordinate system \(xOy\), there is a circle \(C\): \(x^{2}+y^{2}-4y=0\) and a line \(l\): \(x+y-4=0\).  
(1) By establishing a polar coordinate system with the origin \(O\) as the pole and the positive \(x\)-axis as the initial line, find the polar coordinates of the intersection points of circle \(C\) and line \(l\);  
(2) If point \(D\) is the midpoint of the intersection points of circle \(C\) and line \(l\), and the parametric equation of line \(CD\) is \(\begin{cases} x=at+1\\ y=2t+b \end{cases}\) (where \(t\) is the parameter), find the values of \(a\) and \(b\).

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