
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 $xOy$, with $O$ as the pole and the positive $x$-axis as the polar axis, a polar coordinate system is established. The polar equation of curve $C_1$ is $$\rho\cos(\theta- \frac {\pi}{3})=1$$, $P$ is the intersection point of $C_1$ and the $x$-axis. It is known that the parametric equation of curve $C_2$ is $$\begin{cases} x=\cos\theta \\ y=-2+\sin\theta \end{cases}$$ ($\theta$ is the parameter), $M$ and $N$ are two points on curve $C_2$ with corresponding parameters $\theta=\alpha$ and $\theta=\alpha+ \frac {\pi}{2}$, where $\alpha\in\mathbb{R}$.  
(I) Write the Cartesian coordinate equation of curve $C_1$;  
(II) Find the range of values for $|PM|^2+|PN|^2$.

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