
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 equation of line $l$ is $\begin{cases} x=t \\ y=t+1 \end{cases}$ (where $t$ is the parameter), and the parametric equation of curve $C$ is $\begin{cases} x=2+2\cos \phi \\ y=2\sin \phi \end{cases}$ (where $\phi$ is the parameter). Establish a polar coordinate system with $O$ as the pole and the non-negative semi-axis of the $x$-axis as the polar axis.
(I) Find the polar coordinate equations of line $l$ and curve $C$;
(II) It is known that ray $OP$: $\theta_1=\alpha$ (where $0<\alpha<\frac{\pi}{2}$) intersects curve $C$ at points $O$ and $P$, and ray $OQ$: $\theta_2=\alpha+\frac{\pi}{2}$ intersects line $l$ at point $Q$. If the area of $\triangle OPQ$ is $1$, find the value of $\alpha$ and the length of chord $|OP|$.

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