
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 coordinates of the two foci of the ellipse $E$ are $F_1(-2,0)$ and $F_2(2,0)$, and the ellipse passes through the point $P(\frac{5}{2},-\frac{3}{2})$.

(I) Find the standard equation of the ellipse $E$.

(II) The line passing through the left focus $F_1$ of the ellipse intersects the ellipse at two points $A$ and $B$. $O$ is the coordinate origin, and $OA \perp OB$. Find the equation of the line $AB$.

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