
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 rectangular coordinate system $xOy$, the equation of circle $O$ is $x^2+y^2=1$.
(1) Stretch the abscissa to $\sqrt {2}$ times the original, and keep the ordinate unchanged to get the curve $C$. Find the general equation of curve $C$.
(2) It is known that the parametric equation of line $l$ is $\begin{cases} x=1+t\cos\alpha \\ y=t\sin\alpha \end{cases}$ ($t$ is the parameter). Line $l$ intersects curve $C$ at points $A$ and $B$. Find the minimum value of $|AB|$.

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