
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 the polar equation of curve $C$ is $\rho=4\cos \theta$. Establish a Cartesian coordinate system with the pole as the origin and the polar axis as the positive half of the $x$-axis. The parametric equation of the line $l$ is 
$ \begin{cases}
x=1+t\cos \alpha \\
y=t\sin \alpha
\end{cases} $
($t$ is the parameter).
(1) Convert the polar equation of curve $C$ into a Cartesian equation;
(2) If line $l$ intersects curve $C$ at points $A$ and $B$, and $|AB|= \sqrt{14}$, find the value of the inclination angle $\alpha$.

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