
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 equations $\begin{cases} \dfrac{3}{4}{{m}^{2}}-3m+4=m \\ \dfrac{3}{4}{{n}^{2}}-3n+4=n \end{cases}$ are satisfied for $m=\dfrac{4}{3},n=4$, determine the range of values for the real number $2{{x}_{2}}+\dfrac{a}{{{x}_{2}}}-1$ when $m=1,n=4$.

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