
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 rectangular coordinate system $(xOy)$, curve $B$ is a line passing through point $P(-1,1)$ with an inclination angle of $\frac{\pi}{4}$. In the polar coordinate system established with the origin of the rectangular coordinate system $(xOy)$ as the pole and the positive semi-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 ordinary equation of curve $A$ and a parametric equation of curve $B$;
(2) Curves $A$ and $B$ 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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