
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
Given a polar coordinate system with the origin as the pole and the non-negative semi-axis of the $x$-axis as the polar axis, the polar coordinate equation of the line $l$ is $ρ\cos(θ-\frac{π}{4})=5+\sqrt{2}$. The parametric equation of the curve $C$ is $ \begin{cases} x=2+2\cos α \\ y=2\sin α \end{cases}$ ($α$ is the parameter).

1. Write the rectangular coordinate equation of the line $l$ and the general equation of the curve $C$.
2. If point $A$ is on the curve $C$, and point $B$ is represented by $(5\sqrt{2}+\frac{\sqrt{2}}{2}t, 2-\frac{\sqrt{2}}{2}t)$ ($t$ is the parameter), find the minimum value of $|AB|$.

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