
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 the set $A=[{s,s+\frac{1}{6}}]∪[{t,t+1}]$, where $1\notin A$ and $s+\frac{1}{6}＜t$, let $f(x)=\frac{{x+1}}{{x-1}}$. For any $x\in A$, $f\left(x\right)\in A$. Find the value of $s+t$.

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