
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 sets $A=\{x\mid 1\leqslant x\leqslant 4\}$ and $B=\{x\mid m\leqslant x\leqslant m+1\}$.
(1) Find $A\cap B$ and $A\cap B^c$ when $m=3$;
(2) If $A\cap B=B$, find the range of values for the real number $m$.

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