
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 $xOy$, with $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the polar coordinate system is established. The polar coordinate equation of the curve $C$ is $\rho=2\sin\theta+2a\cos\theta$ ($a>0$); the parameter equation of the line $l$ is $$\begin{cases} x=-2+ \frac { \sqrt {2}}{2}t \\ y= \frac { \sqrt {2}}{2}t\end{cases}$$ ($t$ is the parameter), and the line $l$ intersects with the curve $C$ at points $M$ and $N$.
(1) Write the rectangular coordinate equation of the curve $C$ and the normal equation of the line $l$;
(2) If the polar coordinates of point $P$ are $(2,\pi)$, and $|PM|+|PN|=5 \sqrt {2}$, find the value of $a$.

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