
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 B is a line passing through point P(-1, 1) with an inclination angle of $\frac{\pi}{4}$. Taking the origin of the Cartesian coordinate system $xOy$ as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve A is $\rho^{2}= \frac{12}{3+\sin^{2}\theta}$.  
(1) Find the Cartesian equation of curve A and a parametric equation of curve B;  
(2) Curve A and curve B intersect at points M and N, find the value of $|MP|+|NP|$.

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