
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 of the plane, a polar coordinate system is established with the coordinate origin O as the pole and the positive semi-axis of the x-axis as the polar axis. The polar coordinate equation of the straight line l is: $$ρ= \frac {1}{sin(θ- \frac {π}{4})}$$, and the ellipse $$C： \begin{cases} x=2cosθ \\ y= \sqrt {3}sinθ\end{cases}$$.
(I) Find the rectangular coordinate equations of the straight line l and the ellipse C;
(II) If the straight line l intersects the ellipse C at points M and N, and point $$P(0, \sqrt {2})$$, find |PM|+|PN|.

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