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

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