
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 $xOy$, the parametric equation of line $l$ is given by $$\begin{cases} x= \sqrt {3}t \\ y=1+t \end{cases}$$ (where $t$ is the parameter). With the origin $O$ as the pole and the non-negative half-axis of the $x$-axis as the polar axis, the polar equation of curve $C$ is $\rho^2\cos2\theta=1$. Line $l$ intersects curve $C$ at points $A$ and $B$.
(I) Find the length of $|AB|$;
(II) If point $P$ has polar coordinates $(1, \frac{\pi}{2})$, find the distance from the midpoint $M$ of $AB$ to $P$.

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