
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
In the rectangular coordinate system $(xOy)$, the polar coordinate system is established with $O$ as the pole and the positive semi-axis of $x$ as the polar axis. Given the polar coordinate equation of line $l$ as $ρ(\sin θ - 3\cos θ) = 0$, and the parametric equation of curve $C$ as $\begin{cases} x = t - \frac{1}{t} \\ y = t + \frac{1}{t} \end{cases}$ ($t$ is the parameter). Line $l$ intersects curve $C$ at points $A$ and $B$. Calculate the distance $|AB|$.

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