
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 that the parametric equations of curve $C\_1$ are $x=2\cos θ$, $y=\sqrt {3}\sin θ$ (with $θ$ as the parameter), and the polar coordinate equation of curve $C\_2$ is $ρ=2$ with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis.

1. Write out the Cartesian equation of $C\_1$ and the polar coordinate equation of $C\_2$.
2. If $M$ and $N$ are the upper and lower vertices of curve $C\_1$, and $P$ is any point on curve $C\_2$, find the maximum value of $|PM|+|PN|$.

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