
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
Suppose that $f(x)$ is an odd function and a decreasing function on the domain $(-1, 1)$.

(1) Find the set $M$ that satisfies $f(1-a)+f(1-a^{2}) < 0$;

(2) For the $a$ in part (1), find the domain of the function $F(x)=\log_{a}\left[ 1-{\left( \dfrac{1}{a}\right)}^{{x}^{2}-x}} \right]$.

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