
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 sets $A=\{x| -3\leqslant x\leqslant 7\}$ and $B=\{x| t+1\leqslant x\leqslant 2t-2\}$. $(1)$ Choose one of the following conditions, $\complement _{R}A\subseteq \complement _{R}B$, $A\cup B=A$, or $A$⋂$B=B$, and answer the following question. Question: When sets $A$ and $B$ satisfy _____, find the range of $t$. Note: If multiple conditions are chosen and answered separately, the first answer will be scored. $(2)$ If $A\cap B=\varnothing$, find the range of $t$.

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