
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 $$a^{x^{2}-ax-2a^{2}}>1 \quad (a>0 \text{ and } a\neq1)$$ has the solution set $\{x|-a<x<2a\}$ and the function $$f(x)= \sqrt {\left( \frac {1}{a}\right)^{x^{2}+2mx-m}-1}$$ has the domain of $\mathbb{R}$, determine the range of $m$.

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