
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 $$\begin{cases} x=t \\ y=t+2 \end{cases}$$ (where $t$ is the parameter). Establish a polar coordinate system with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of circle $C$ is $$ρ= \sqrt {2}\cos(θ+ \frac {π}{4})$$.

(1) Find the rectangular coordinates of the center of circle $C$.
(2) Draw a tangent line to circle $C$ through line $l$ and find the minimum length of the tangent line segment.

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