
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 $A=\{x| -3 \leqslant x \leqslant 4\}$ and $B=\{x| 1-m \leqslant x \leqslant 3m-2, m > 1\}$, is there a real number $m$ such that $x \in A$ implies $x \in B$?  
$(1)$ Determine the necessary and sufficient condition for the existence of a real number $m$ such that $x \in A$ implies $x \in B$. If it exists, find the value of $m$; if not, explain the reason.  
$(2)$ Choose between the conditions of "sufficient but not necessary" and "necessary but not sufficient" to supplement the blank in the above question. If the real number $m$ exists in the question, find the range of values for $m$; if not, explain the reason.

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