
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
An ellipse has the equation $$\frac {x^{2}}{a^{2}}$$+ $$\frac {y^{2}}{b^{2}}$$\=1 (a > b > 0). Its center is O, and its left and right vertices are A and B, respectively. The distance from point A to the right focus is 3, and the eccentricity is $$\frac {1}{2}$$. P is any point on the ellipse that does not coincide with points A and B.

1. Find the equation of the ellipse.
2. Let Q(0, -m) (m > 0) be a fixed point on the y-axis. When point P moves on the ellipse, and the maximum value of PQ is $$\sqrt {5}$$, find the value of m.

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