
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
Find the length of segment AB, where AB is the segment between points A and B where the line passing through point \( P(-3, 0) \) with an incline angle of \( 30^\circ \) intersects the curve defined by the parametric equations:
\[ 
\begin{cases} 
x = t + \frac {1}{t} \\ 
y = t - \frac {1}{t}
\end{cases} 
\]
\( t \) is the parameter.

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