
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 rectangular coordinate system $(xOy)$, the parametric equations of line $l$ are $\begin{cases} x=\frac{\sqrt{2}}{2}t \\ y=\frac{\sqrt{2}}{2}t \end{cases} (t \text{ is the parameter})$, and the equation of circle $C$ is $x^{2}+y^{2}-4x-2y+4=0$. Establish a polar coordinate system with $O$ as the pole and the positive half of the $x$-axis as the polar axis.

(1) Find the Cartesian equation and polar equation of line $l$ and the polar equation of circle $C$;
(2) Given that line $l$ intersects with circle $C$ at points $P$ and $Q$, find the distance $|PQ|$.

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