
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.\\) Taking the pole as the origin of the Cartesian coordinate system, and the polar axis as the positive half-axis of \\(x\\), establish a Cartesian coordinate system. The parametric equation of line \\(m\\) is \\(\begin{cases}x=1+t\cos \alpha \\ y=t\sin \alpha\end{cases} \\) (where \\(t\\) is the parameter).

\\((1)\\) Convert the polar equation of curve \\(C\\) into a Cartesian coordinate equation;

\\((2)\\) If line \\(m\\) intersects curve \\(C\\) at points \\(A\\) and \\(B\\), and \\(|AB|= \sqrt{14} \\), find the value of the inclination angle \\(\alpha\\) of line \\(m\\).

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