
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 quadratic inequality about $x$, $ax^{2}-ax-2a^{2} > 1 (a > 0, a \neq 1)$, the solution set is $\{x|-a < x < 2a\}$ and the domain of the function $f(x)=\sqrt{\left(\frac{1}{a}\right)^{x^{2}+2mx-m} -1}$ is $\mathbb{R}$, determine the range of values for $m$.

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