
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
Given the polar equation of line $l$ as $\sqrt{2}\rho\cos\left(\theta + \frac{\pi}{4}\right) = -1$, and the parametric equation of curve $C$ is $\begin{cases} x=t \\ y=t^2 \end{cases}$ (where $t$ is a parameter). Taking the pole as the origin and the polar axis as the positive direction of the x-axis, let point M be $\left(\frac{1}{2} - \frac{\sqrt{5}}{2}, \frac{1}{2} - \frac{\sqrt{5}}{2}\right)$. Line $l$ intersects curve $C$ at points $A$ and $B$.  
(I) Find the standard form equations of line $l$ and curve $C$.  
(II) Calculate the value of $|MA|^2 \cdot |MB|^2$.

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