
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, it is known that the circle $C$ has its center at $C(\sqrt{2}, \frac{\pi}{4})$ and radius $r=\sqrt{3}$.
- (I) Find the polar equation of circle $C$;
- (II) If $\alpha \in [0, \frac{\pi}{4})$, the parametric equation of line $l$ is $\begin{cases} x=2+t\cos \alpha \\ y=2+t\sin \alpha \end{cases}$ (where $t$ is the parameter), line $l$ intersects circle $C$ at points $A$ and $B$, find the range of the chord length $|AB|$.

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