
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
The ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$) has its left and right foci at $F_1(-c,0)$ and $F_2(c,0)$, respectively. The minimum distance from point $F_1$ to the ellipse is $1$, and the maximum distance from point $F_1$ to the ellipse is $3$.

(Ⅰ) Find the equation of the ellipse;

(Ⅱ) Given that the vertices $A$ and $C$ of the rhombus $ABCD$ are on the ellipse $C_1$, and the vertices $B$ and $D$ are on the line $7x-7y+1=0$, find the equation of line $AC$.

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