
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 function $f(x)=\sqrt{a{x^2}-2ax+1}$ with the domain of $R$, where $a$ is a real number.<br/>$(Ⅰ)$ Find the range of values for $a$;<br/>$(Ⅱ)$ When $a=1$, does there exist a real number $m$ such that for any $x_{1}\in \left[-1,1\right]$, there exists $x_{2}\in R$ satisfying the inequality ${9^{{x_1}}}+{9^{-{x_1}}}+m({{3^{{x_1}}}-{3^{-{x_1}}}})-1≥f({{x_2}})$? If it exists, find the range of values for the real number $m$; if not, please explain the reason.

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