
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, with the origin as the pole and the non-negative half-axis of the _x_-axis as the polar axis, a polar coordinate system is established. The parametric equation of line _l_ is given by:
\[
\begin{cases}
x= \frac{ \sqrt{2}}{2}t \\
y=2+ \frac{ \sqrt{2}}{2}t
\end{cases}
\]
(where _t_ is the parameter), and the polar equation of curve _C_ is $\rho=4$.

(1) If in the parametric equation of _l_, $t=- \sqrt{2}$, find the polar coordinates of point _M_ obtained and the Cartesian equation of curve _C_;

(2) If point _P(0,2)_, 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}
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