
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 equation of line $l$ is $\sqrt {3}x-y+2 \sqrt {3}=0$. Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar equation of the curve $C$ is $\rho=2(\sin{\theta}+\cos{\theta})$.

1. Find the Cartesian equation of curve $C$.
2. Draw a perpendicular line from point $P(1,0)$ to line $l$, intersecting curve $C$ at points $M$ and $N$. Find the value of $\frac {1}{|PM|}+ \frac {1}{|PN|}$.

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