
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 that the solution set of the inequality $x^{2}-5ax+b \gt 0$ is $\{x\left|\right.x \gt 4$ or $x \lt 1\}$.  
$(I)$ Find the values of real numbers $a$ and $b$;  
$(II)$ If positive real numbers $x$ and $y$ satisfy $x+y=2$, $t=\frac{a}{x}+\frac{b}{y}$, find the minimum value of $t$.

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