
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, the parametric equations of line $l$ are given by $\begin{cases} x = -\frac{\sqrt{2}}{2}t \\ y = -4 + \frac{\sqrt{2}}{2}t \end{cases}$ (where $t$ is the parameter). With the origin as the pole and the positive half of the $x$-axis as the polar axis, a coordinate system is established. The polar equation of curve $C$ is given by $\rho = 4\cos{\theta}$.

(1) Write the Cartesian equation of line $l$ and curve $C$.
(2) Through point $M(1,0)$, a line $l'$ is drawn parallel to line $l$, intersecting curve $C$ at points $A$ and $B$. Find the length $|AB|$.

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