
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 equation of line $l$ is $$\begin{cases} x= \frac { \sqrt {2}}{2}t \\ y=2+ \frac { \sqrt {2}}{2}t\end{cases}$$ (where $t$ is the parameter). In the polar coordinate system established with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the polar coordinate equation of circle $C$ is $\rho=4\cos\theta$. Let $M$ be any point on circle $C$, and connect $OM$ and extend it to $Q$ such that $|MQ|=2|OM|$.
(1) Find the rectangular coordinate equation of the trajectory of point $Q$;
(2) If line $l$ intersects with the trajectory of point $Q$ at points $A$ and $B$, point $P$ has rectangular coordinates $(0,2)$, find the value of $|PA|+|PB|$.

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