
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 general term formula of a sequence ${a_n=an^2+n+5}$, where ${a_1 < a_2 < a_3 < a_4}$ and ${a_n > a_{n+1}}$ holds true for all ${n \geqslant 8}$, determine the range of values for the real number ${a}$.

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