
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 $C$: $(x+1)^2 + y^2 = 8$, and a point $A(1,0)$, let $P$ be any point on circle $C$. The perpendicular bisector of segment $AP$ intersects line $CP$ at point $Q$. As point $P$ moves on the circle, point $Q$ traces curve $E$.
1. Find the equation of curve $E$.
2. If the straight line $l$: $y=kx+m$ intersects curve $E$ at points $M$ and $N$, and $O$ is the origin, find the maximum value of the area of $\triangle MON$.

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