
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 that the eccentricity of the ellipse $C$ with foci on the $x$-axis is $\frac{\sqrt{3}}{2}$, and it passes through the point $A(-2,1)$.

(1) Find the standard equation of the ellipse $C$;

(2) Line $l:x-y+2=0$ intersects the ellipse $C$ at points $P$ and $Q$, with $O$ being the origin, find the area of $\Delta OPQ$.

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