
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 a line $l$ with parameter equations:
$$
\begin{cases}
x = t \\
y = t - 2
\end{cases} \quad (t \text{ is a parameter})
$$
and a curve $C$ with parameter equations:
$$
\begin{cases}
x = 2\cos\theta \\
y = 2\sin\theta
\end{cases} \quad (\theta \text{ is a parameter})
$$
where $l$ intersects the curve $C$ at points $A$ and $B$, find the length of the segment $|AB|$.

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