
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 the sequences \((a_n)\) and \((b_n)\) be defined by
\[a_{n + 1} = \frac{a_n^2}{b_n} \quad \text{and} \quad b_{n + 1} = \frac{b_n^2}{a_n}\] for all \(n \ge 0.\) Find \(b_7\) in the form \(\frac{4^p}{3^q}\) for some integers \(p\) and \(q.\)

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