
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 cartesian coordinate system $(xOy)$, a pole is established at the coordinate origin $O$ with the positive semi-axis of $x$ as the polar axis to create a polar coordinate system. The parametric equations of the curve $C_1$ are given by $ \begin{cases} x= \frac {1}{2}\cos α \\ y=1+ \frac {1}{2}\sin α \end{cases}(α \text{ is the parameter})$, and the polar coordinate equation of the curve $C_2$ is given by $ρ^{2}(\sin ^{2}θ+4\cos ^{2}θ)=4$.

1. Find the general equations of the curves $C_1$ and $C_2$.
2. If $A$ is any point on the curve $C_1$, and $B$ is any point on the curve $C_2$, find the minimum value of $|AB|$.

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