
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
The polar equation of the conic curve C is: $\rho^2(1+\sin^2\theta)=2$.  
(1) Establish a Cartesian coordinate system with the pole as the origin and the polar axis as the non-negative half of the x-axis. Find the Cartesian equation of curve C, and determine the coordinates of the focus of curve C in the Cartesian coordinate system and in the polar coordinate system;  
(2) The polar equation of line l is $\theta= \frac{\pi}{3}$ ($\rho\in\mathbb{R}$). If the distance from point M on curve C to line l is maximum, find the coordinates of point M (both Cartesian and polar coordinates are acceptable).

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