
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
Given the polar equation of curve $C_1$ is $\rho^2=\frac {2}{3+\cos2\theta}$, establish a rectangular coordinate system with the pole O as the origin and the polar axis as the positive direction of the x-axis. After stretching all the x-coordinates of points on curve $C_1$ to twice their original values and shortening all the y-coordinates to half of their original values, we obtain curve $C_2$.
1. Write down the rectangular coordinate equation of curve $C_1$.
2. Take any point R on curve $C_2$ and find the maximum distance from point R to the line $l: x + y - 5 = 0$.

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