
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 the sequence ${a_n}$ as $a_n=2q^n+q$ where $(q < 0, n \in \mathbb{N^{*}})$, if for any $m$, $n \in \mathbb{N^{*}}$ it holds that $\frac{a_m}{a_n} \in \left(\frac{1}{6}, 6\right)$, then find the range of values for the real number $q$.

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