
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 Cartesian coordinate system $xOy$, the parametric equation of curve $C$ is
$$
\begin{cases}
x = \sin \alpha + \cos \alpha, \\
y = \sin \alpha - \cos \alpha
\end{cases}
\quad (\alpha \text{ is the parameter}).
$$
(1) Find the general equation of curve $C$;  
(2) In the polar coordinate system with $O$ as the pole and the positive $x$-axis as the polar axis, the equation of line $l$ is $\sqrt{2}\rho\sin \left( \dfrac{\pi}{4} - \theta \right) + \dfrac{1}{2} = 0$. It is known that the line $l$ intersects the curve $C$ at points $A$ and $B$. Find $|AB|$.

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