
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, there exists an ellipse C with equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$) and eccentricity $\frac{\sqrt{3}}{2}$. The length of the chord intercepted by line $l_1: \frac{x}{a} + \frac{y}{b} = 1$ on ellipse C is $\sqrt{5}$.
1. Determine the standard equation of ellipse C.
2. If line $l_1$ is tangent to the circle D: $x^2 + y^2 - 6x - 4y + m = 0$:
   i. Find the standard equation of circle D.
   ii. If line $l_2$ passes through the fixed point (3, 0), intersects ellipse C at two different points E and F, and intersects circle D at two different points M and N, determine the range of values for |EF|•|MN|.

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