
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
A two-digit positive integer $m$, if $m$ satisfies that the digits on each digit are different and not equal to $0$, then $m$ is called a "special number". Let $m_{1}$ be the number obtained by swapping the two digits of $m$. Put $m_{1}$ after $m$ to form the first four-digit number, and put $m$ after $m_{1}$ to form the second four-digit number. Let the quotient obtained by subtracting the second four-digit number from the first four-digit number and then dividing by $99$ be denoted as $F(m)$. For example, when $m=34$, $m_{1}=43$, $F(34)=\frac{{3443-4334}}{{99}}=-9$, then $F(38)=\_\_\_\_\_\_$. If $s$ and $t$ are both "special numbers", where $s=10a+b$ and $t=10x+y$ ($1\leqslant b \lt a\leqslant 7$, $1\leqslant x\leqslant 8$, $1\leqslant y\leqslant 8$, and $a$, $b$, $x$, $y$ are integers), define: $Q(s,t)=\frac{{t-s}}{s}$. If $F(s)$ satisfies a remainder of $1$ when divided by $5$, and $F(t)-F(s)+18x=36$, then the minimum value of $Q(s,t)$ is ______.

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