
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 Cartesian coordinate system, and the polar axis coincides with the positive half-axis of the _x_ axis in the Cartesian coordinate system. If the parametric equation of curve _C_ is $\begin{cases}x=3+3\cos \alpha \\ y=2\sin \alpha\end{cases}$ (where $\alpha$ is the parameter), and the polar equation of line _l_ is $\sqrt{2} \rho \sin \left(\theta- \frac{\pi}{4} \right)=1$.  
(1) Convert the parametric equation of curve _C_ into a polar equation;  
(2) Draw a tangent from a point on line _l_ to curve _C_, and find the minimum length of the tangent.

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