
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 $A=\{ x|x\leqslant -1\}$ or $x\geqslant 3\}, B=\{ x|1\leqslant x\leqslant 6\}, C=\{ x|m+1\leqslant x\leqslant 2m\}$.  
(Ⅰ) Find $A\cap B$.  
(Ⅱ) If $B\cup C=B$, find the range of the real number $m$.

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