
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, curve C<sub>1</sub> is given by $$\begin{cases} x=\cos\theta \\ y=\sin\theta\end{cases}$$ (where $\theta$ is a parameter). Taking the origin O of the Cartesian coordinate system xOy as the pole and the positive half-axis of x as the polar axis, and using the same unit length to establish a polar coordinate system, the line l is given by $\rho(2\cos\theta-\sin\theta)=6$.

(1) Find the Cartesian equations for C<sub>1</sub> and line l.  
(2) Find a point P on curve C<sub>1</sub> such that the distance from point P to line l is minimized, and calculate this minimum distance.

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