
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 an ellipse $$C: \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a > b > 0)$$ with two foci $$F_{1}, F_{2}$$, and $$|F_{1}F_{2}| = 2\sqrt{2}$$, points A and B are on the ellipse, with $F_{1}$ on segment AB, and the perimeter of △ABF<sub>2</sub> equals $$4\sqrt{3}$$.
(1) Find the standard equation of ellipse C;
(2) For any point P on the circle O: $x^{2} + y^{2} = 4$, draw two tangents to ellipse C, PM and PN, intersecting circle O at points M and N, respectively. Find the maximum area of △PMN.

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