
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 that the arithmetic sequence ${a_n}$ has a common difference $d$ not equal to 0, and the geometric sequence ${b_n}$ has a common ratio $q$ that is a positive rational number less than 1. If $a_1 = d$, $b_1 = d^2$, and $$\frac{a_1^2 + a_2^2 + a_3^2}{b_1 + b_2 + b_3}$$ is a positive integer, find the value of $q$.

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