
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 that the pole of the polar coordinate system coincides with the origin of the rectangular coordinate system, and the polar axis coincides with the positive semi-axis of the $x$-axis in the rectangular coordinate system. If the parametric equations of the curve $C$ are $ \begin{cases} x=3+2\cos \alpha \\ y=2\sin \alpha \end{cases} (\alpha \text{ is the parameter})$, and the polar coordinate equation of the line $l$ is $ \sqrt {2}\rho\sin (θ- \frac {π}{4})=1$.

1. Convert the parametric equations of the curve $C$ into polar coordinate equations.
2. A tangent line is drawn from a point on the line $l$ to the curve $C$. Find the minimum length of the tangent line.

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