
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 the plane rectangular coordinate system $(xOy)$, the polar coordinate system is established with the origin $O$ as the pole and the non-negative semi-axis of the $x$-axis as the polar axis. The polar coordinate equation of the line $l$ is $\rho \cos \left(\theta - \frac{\pi }{4}\right)=2 \sqrt{2}$, and the polar coordinate equation of the circle $C$ is $\rho =4\sin \theta$.
(I) Find the polar coordinates of the intersection point of $l$ and $C$;
(II) Let $P$ be the center of $C$, $Q$ be the midpoint of the line segment connecting the intersection points of $l$ and $C$, and it is known that the parametric equation of line $PQ$ is $\begin{cases} x=3t+a \\ y=\frac{b}{2}3t+1 \end{cases} (t \text{ is the parameter})$, find the values of $a$ and $b$.

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