
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 a moving circle P is tangent to the circle $F_1: (x+2)^2+y^2=49$ and internally tangent to the circle $F_2: (x-2)^2+y^2=1$, denote the trajectory of the center P as curve C.  
(Ⅰ) Find the equation of curve C;  
(Ⅱ) Let Q be a moving point on curve C that is not on the x-axis, O be the origin, and draw a line parallel to OQ through point $F_2$ intersecting curve C at two distinct points M and N. Find the maximum area of $\triangle QMN$.

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