
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 $A=\{y|y= \sqrt {3-2x},x\in[- \frac {13}{2}, \frac {3}{2}]\}$ and $B=\{x|1-m\leqslant x\leqslant m+1\}$.
$(1)$ If $m=2$, find $A\cap B$;
$(2)$ If $B\subseteq A$, find the range of values for $m$.

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