
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 proposition: "There exists an $x \in [-1, 1]$ such that the equation $m = x^2 - x$ holds true," is a true statement.
1. Determine the set of real numbers $M$ for which $m$ can take values.
2. Suppose the solution set to the inequality $(x - a)[x - (2 - a)] < 0$ is $N$. If $N \subseteq M$, determine the range of values for $a$.

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