
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 center of an ellipse is at the origin, its foci lie on the x-axis, its eccentricity is $\frac{\sqrt{3}}{2}$, and it passes through point P($-\sqrt{3}, \frac{1}{2}$).
(1) Find the standard equation of the ellipse.
(2) A line $l$ with slope 1 passes through the right focus of the ellipse and intersects the ellipse at points A and B. Find the length of chord AB.

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