
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 $x$ within the set $\{x|-1 < x < 1\}$ such that the equation $x^{2}-x-m=0$ holds" is true.

(1) Find the set $M$ of the real numbers $m$;

(2) Let the solution set of the inequality $(x-a)(x+a-2) < 0$ be $N$. If $x \in N$ is a necessary condition for $x \in M$, find the range of the real number $a$.

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