
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 a Cartesian coordinate system, establish a polar coordinate system with the origin as the pole and the non-negative half-axis of the x-axis as the polar axis. The parametric equations of line $l$ are
$$
\begin{cases}
x= \frac { \sqrt {2}}{2}t \\
y=2+ \frac { \sqrt {2}}{2}t
\end{cases}
$$
($t$ is the parameter), and the polar equation of curve $C$ is $\rho=4$.
(1) When $t=- \sqrt {2}$ in the parametric equations of line $l$, point M is obtained. Find the polar coordinates of M and the Cartesian equation of curve C.
(2) If point P is (0, 2), and line $l$ intersects curve C at points A and B, find $\frac {1}{|PA|}+ \frac {1}{|PB|}$.

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