
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 polar coordinate system, the polar equation of curve C is $${{\rho }^{2}}\left( 1+2{si}{{{n}}^{2}} \theta \right)=3$$, and a Cartesian coordinate system is established with the pole as the origin and the positive half of the polar axis as the x-axis. The parametric equations of line l are $$\begin{matrix} x=t \\ y=6+t \end{matrix}$$ (t is the parameter).
(1) Write the parametric equations of curve C and the general equation of line l.
(2) Given that point P is a point on curve C, find the minimum distance from point P to line l.

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