
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 that in the polar coordinate system, the polar coordinate equation of line l is $ρcos(θ+ \frac {π}{6})= \frac { \sqrt {3}-1}{2}$, and the polar coordinate equation of curve C is ρ(1-$cos^2θ$)-2$cosθ$=0. Establish a plane rectangular coordinate system with the pole as the origin and the polar axis as the positive semi-axis.
(1) Write the rectangular coordinate equations of line l and curve C;
(2) If line l': $y= \sqrt {3}(x-2)$ intersects curve C at points P and Q, and M(2,0), find the value of $|MP|^2+|MQ|^2$.

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