
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 $A=\{x\mid a\leqslant x\leqslant a+9\}$, $B=\{x\mid 8-b < x < b\}$, and $M=\{x\mid x < -1,\text{ or } x > 5\}$,
(1) Find the range of values for the real number $a$ if $A\cup M=R$;
(2) Find the range of values for the real number $b$ if $B\cup (\lnot_{R}M)=B$.

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