
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 Cartesian coordinate system xOy, the parametric equation of line $C_1$ is $$\begin{cases} x=1+t \\ y=1-t\end{cases}$$ (where $t$ is the parameter); with O as the pole and the positive x-axis as the polar axis, the polar equation of curve $C_2$ is $\rho=1$.  
(1) Find the Cartesian equation of curve $C_2$, explain what curve it represents, and write its parametric equation;  
(2) Draw tangents from points on line $C_1$ to curve $C_2$, and find the minimum length of the tangent.

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