
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 of circle $P$ 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. A line parallel to $OQ$ passing through point $F_{2}$ intersects curve $C$ at two distinct points $M$ and $N$. Find the maximum value of the area of $\triangle QMN$.

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