
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 line $l$ passing through the point $(1, 0)$ with an inclination angle of $\alpha$, in the Cartesian coordinate system $xOy$, with $O$ as the pole and the positive half-axis of $x$ as the polar axis, the equation of curve $M$ in the polar coordinate system is $\rho\sin^2\theta+4\cos\theta=0$.  
(1) Write the Cartesian coordinate equation of curve $M$ and the parametric equation of line $l$;  
(2) If line $l$ has only one common point with curve $M$, find the value of the inclination angle $\alpha$.

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