
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 coordinate system with the origin $O$ as the pole and the positive half of the $X$-axis as the polar axis, and the same unit length for both coordinate systems. The parametric equations of line $L$ are $ \begin{cases} x=1+t\cos α \\ y=t\sin a \end{cases} (t$ is the parameter, $0 < a < π$), and the polar equation of curve $C$ is $ρ\sin ^{2}θ=4\cos θ$.
(1) Find the Cartesian equation of curve $C$.
(2) If line $L$ intersects curve $C$ at points $A$ and $B$, and the distance $|AB|=8$, find the value of $α$.

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