
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
A line passes through the point $(-2, \sqrt{3})$ at an angle of inclination of $\frac{\pi}{3}$. Find the parametric equation of the line, and if it intersects the curve $y^2 = -x - 1$ at points A and B, find the length $|AB|$.

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