
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 circle with center at point $M$ and a fixed point $N(1,0)$, where the equation of the circle is $(x+1)^{2}+y^{2}=16$. Point $P$ moves along the circumference of the circle, and point $Q$ is on line segment $NP$. Point $G$ is on line segment $MP$ such that $\overrightarrow{NP}=2\overrightarrow{NQ}$ and $\overrightarrow{GQ}\cdot\overrightarrow{NP}=0$. Let the locus of point $G$ be curve $C$.

1. Find the equation of curve $C$.
2. If line $l$: $y=kx+m$ intersects curve $C$ at points $A$ and $B$, and $k_{OA}\cdot k_{OB}=-\frac{3}{4}$, determine if the area of $\triangle AOB$ is a constant value. If it is, find the value; if not, explain why.

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