
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, establish a polar coordinate system with the coordinate origin as the pole and the non-negative semi-axis of the $x$-axis as the polar axis. Given that point $A$ has polar coordinates $(\sqrt{2}, \frac{\pi}{4})$, and the parametric equations of line $l$ are $\begin{cases} x = \frac{3}{2} - \frac{\sqrt{2}}{2}t \\ y = \frac{1}{2} + \frac{\sqrt{2}}{2}t \end{cases}$ (where $t$ is the parameter), and point $A$ lies on line $l$.
(I) Find the parameter $t$ corresponding to point $A$;
(II) If the parametric equations of curve $C$ are $\begin{cases} x = 2\cos \theta \\ y = \sin \theta \end{cases}$ (where $\theta$ is the parameter), and line $l$ intersects curve $C$ at points $M$ and $N$, find $|MN|$.

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