
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 system, the parametric equation of line $l$ is $$\begin{cases} x=2+ \frac { \sqrt {2}}{2}t \\ y= \frac { \sqrt {2}}{2}t\end{cases}$$ (where $t$ is the parameter). Now, establishing a polar coordinate system with the origin as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C$ is $\rho=8\cos\theta$.  
(1) Write the standard equation of line $l$ and the Cartesian coordinate equation of curve $C$;  
(2) A line $l_1$ passing through point $P(-1,0)$ and parallel to line $l$ intersects curve $C$ at points $A$ and $B$;  
① Find the value of $|AB|$;  
② Find the value of $|PA|+|PB|$;  
③ If the midpoint of segment $AB$ is $Q$, find the value of $|PQ|$ and the coordinates of point $Q$.

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