
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 ellipse $c: \frac {x^{2}}{a^{2}} + \frac {y^{2}}{b^{2}} = 1$ ($a > b > 0$), the two foci are $F_1$ and $F_2$, with the top vertex $A(0, b)$. Triangle $\triangle AF_1F_2$ is an equilateral triangle, and its perimeter is 6.
1. Determine the standard equation of the ellipse $C$ and its eccentricity.
2. Let $O$ be the origin, and $P$ be a moving point on the line $F_1A$. Find the minimum value of $|PF_2|+|PO|$, and the coordinates of point $P$ when this minimum is achieved.

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