
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 $A=\{x\mid -3 < x\leqslant 6\}$, $B=\{x\mid b-3 < x < b+7\}$, $M=\{x\mid -4\leqslant x < 5\}$, and the universal set $U=R$.
1. Find $A\cap M$;
2. If $B\cup (\lnot\_UM)=R$, find the range of values for the real number $b$.

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