
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 statement: "For all $x$ in the set ${ x | -1 \leqslant x \leqslant 1 }, the inequality ${x^{2}}-x-m < 0$ holds true," which is a true statement.

(1) Find the set $B$ of all possible real number values for $m$;

(2) Let the solution set $A$ for the inequality $\left( x-3a \right)\left( x-a-2 \right) < 0$ (where $a < 1$) be given. If $x \in A$ is a sufficient but not necessary condition for $x \in B$, find the range of possible real number values for $a$.

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