
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 $xOy$, the parametric equations of line $l$ are $$\begin{cases} x=1+ \frac { \sqrt {3}}{2}t， \\ y=1+ \frac {1}{2}t\end{cases}$$ ($t$ is the parameter). Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of curve $C$ is $\rho^2-4\rho\cos\theta-2\rho\sin\theta+1=0$, and the polar coordinates of point $M$ are ($ \sqrt {2}$, $ \frac {\pi}{4}$).

(I) Write the rectangular equation of curve $C$ and the rectangular coordinates of point $M$;

(II) Suppose line $l$ intersects curve $C$ 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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