
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 parabola $C$: $y^{2}=2px (p > 0)$ with a point $M(x_{0},y_{0})$ on it, the minimum distance from $M$ to point $N(2,0)$ is $\sqrt{3}$.

1. Find the equation of parabola $C$.
2. If $x_{0} > 2$, a circle $E$: $(x-1)^{2}+y^{2}=1$. Two tangent lines are drawn from $M$ to circle $E$, intersecting the $y$-axis at points $A(0,a)$ and $B(0,b)$. Find the minimum area of $\triangle MAB$.

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