
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 point $P$ on the ellipse $E$: $\frac{x^2}{4} + y^2 = 1$, and $F_1$, $F_2$ are its two foci, with $O$ being the origin. A moving point $Q$ satisfies $\overrightarrow{OQ} = \overrightarrow{PF_1} + \overrightarrow{PF_2}$.

(Ⅰ) Find the trajectory equation of the moving point $Q$;

(Ⅱ) If point $A(0,-2)$ is known, and a line $l$ passing through point $A$ intersects the ellipse $E$ at points $B$ and $C$, find the maximum value of the area of $\triangle OBC$.

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