
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
Let \(a_0 = 3\), \(b_0 = 4\), and
\[a_{n + 1} = \frac{a_n^3}{b_n^2} \quad \text{and} \quad b_{n + 1} = \frac{b_n^3}{a_n^2}\] for all \(n \ge 0.\) Then \(b_8 = \frac{4^p}{3^q}\) for some integers \(p\) and \(q.\) Find the ordered pair \((p, q).\)

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