
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 polar coordinate system, the center of circle $C$ is given by $C(\sqrt{2},\frac{\pi}{4})$ and its radius is $r=\sqrt{3}$.
(I) Find the polar coordinate equation of circle $C$.
(II) If $\alpha\in[0,\frac{\pi}{4})$, the parametric equations of line $l$ are given by $\begin{cases} & x=2+t\cos\alpha \\ & y=2+t\sin\alpha \end{cases}$ (with $t$ as the parameter). Find the range of chord length $|AB|$, where $A$ and $B$ are the points of intersection between line $l$ and circle $C$.

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