
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 inequality in terms of $x$, $ax^2 - ax - 2a^2 > 1$ $(a > 0, a \neq 1)$, has a solution set of $(-a, 2a)$, and the domain of the function $f(x) = \sqrt{\left(\frac{1}{a}\right)^{x^2+2mx-m} -1}$ is $\mathbb{R}$, then the range of values for the real number $m$ is ______.

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