
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 \(a_0 = 3\), \(b_0 = 5\), and define the sequences \(a_n\) and \(b_n\) for \(n \geq 0\) by
\[
a_{n+1} = \frac{b_n^2}{a_n} \quad \text{and} \quad b_{n+1} = \frac{a_n^2}{b_n}.
\]
Find \(a_8\) in the form \(\frac{5^m}{3^n}\) for some integers \(m\) and \(n\), and determine the ordered pair \((m, n)\).

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