
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: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ (with $a > b > 0$), the length of the minor axis is half the length of the major axis. The shortest distance from a point on the ellipse C to the right focus F is $2 - \sqrt{3}$. The line $l: y = x + m$ intersects the ellipse C at two distinct points A$(x_1, y_1)$ and B$(x_2, y_2)$.
(Ⅰ) Find the equation of the ellipse C;
(Ⅱ) If the area of triangle $\triangle AOB$ is 1, find the equation of line $l$.

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