
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
Let $A=\{x | -2 \leq x \leq 2\}$, $B=\{x | 1-m \leq x \leq 2m-2\}$.  
$(1)$ If $x \in A$ is a sufficient but not necessary condition for $x \in B$, find the range of real number $m$;  
$(2)$ If $A \cap B = B$, find the range of real number $m$.

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