
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]


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Given that the foci of an ellipse are $F\_1(0,-1)$ and $F\_2(0,1)$, and the eccentricity $e= \frac {1}{2}$,
(I) Find the standard equation of this ellipse;
(II) Suppose point $P$ is on this ellipse, and $|PF\_1|-|PF\_2|=1$, find the cosine value of $∠F\_1PF\_2$.

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