
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 line \( l \) is
\[\begin{cases}
x = t \cos \alpha \\
y = 1 + t \sin \alpha
\end{cases}\]
(where \( t \) is the parameter, \( 0 \leq \alpha < \pi \)). Taking the origin as the pole and the positive part of the x-axis as the initial line, a polar coordinate system is established. It is known that the polar equation of curve \( C \) is \( \rho \cos^2 \theta = 4 \sin \theta \).

(1) Find the Cartesian equations of line \( l \) and curve \( C \).
(2) Assume line \( l \) intersects curve \( C \) at distinct points \( A \) and \( B \). If \( |AB| = 8 \), find the value of \( \alpha \).

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