
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 vectors $\overrightarrow{a}=(m,-1)$ and $\overrightarrow{b}=(\frac{1}{2},\frac{\sqrt{3}}{2})$,

(I) If $m=-\sqrt{3}$, find the angle $\theta$ between $\overrightarrow{a}$ and $\overrightarrow{b}$;

(II) Suppose $\overrightarrow{a}$ is perpendicular to $\overrightarrow{b}$.

1. Find the value of the real number $m$;
2. If there exist non-zero real numbers $k$ and $t$ such that $[\overrightarrow{a}+(t^{2}-3)\overrightarrow{b}]\perp (-k\overrightarrow{a}+t\overrightarrow{b})$, find the minimum value of $\frac{k+t^{2}}{t}$.

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