
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 two points $F_1(-2, 0)$, $F_2(2, 0)$, a moving point $M$ on curve $C$ satisfies $|MF_1| + |MF_2| = 2|F_1F_2|$, the line $MF_2$ intersects curve $C$ at another point $P$.  
(Ⅰ) Find the equation of curve $C$;  
(Ⅱ) Let $N(-4, 0)$, if the ratio of the areas $S_{\triangle MNF_{2}}:S_{\triangle PNF_{2}} = 3:2$, find the equation of line $MN$.

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