
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 an ellipse $C_1$: $$\frac{x^{2}}{4} + \frac{y^{2}}{3}= 1,$$ with its left directrix denoted by $l_1$, and its right directrix denoted by $l_2$. Let a parabola $C_2$ have the origin $O$ as its vertex and $l_2$ as its directrix. The parabola $C_2$ intersects the line $l_1$ at points $A$ and $B$.
(1) Find the standard equation of the parabola $C_2$.
(2) Calculate the length of the line segment $AB$.

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