
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 the curve $C$ with the polar coordinate equation $ρ = 2 \cos θ - 4 \sin θ$. Establish a Cartesian coordinate system with the pole as the origin and the positive half of the polar axis as the $x$-axis. The parametric equations of line $l$ are given by $ \begin{cases} x = 1 + t \\ y = -1 + t \end{cases} (t \text{ is the parameter})$.
1. Determine the positional relationship between line $l$ and curve $C$, and explain the reasoning.
2. If line $l$ intersects curve $C$ at points $A$ and $B$, find the length $|AB|$.

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