
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 $xy$, the curve $C_1$ has the parametric equations $x = 2 - \sqrt{2}t$ and $y = -1 + \sqrt{2}t$ (with $t$ as the parameter). In the polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis, the curve $C_2$ has the polar equation $\rho = \frac{2}{\sqrt{1+3\sin^2\theta}}$.
(1) Find the Cartesian equation for curve $C_1$ and the Cartesian equation for curve $C_2$.
(2) Let point $M$ be $(2,-1)$, and assume that $C_1$ and $C_2$ intersect at points $A$ and $B$. Find the value of $|MA|\cdot|MB|$.

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