
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 $(xOy)$, a polar coordinate system is established with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis. It is known that the point $P( \sqrt {2}, \frac {7π}{4})$ is on the line $l$: $ρ\cos θ+2ρ\sin θ+a=0(a∈R)$.

(I) Find the rectangular coordinate equation of line $l$.

(II) If point $A$ is on line $l$ and point $B$ is on the curve $C$: $ \begin{cases} x=t \ y= \frac {1}{4}t^{2}\end{cases}(t$ is the parameter$)$, find the minimum value of $|AB|$.

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