
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 \( a_0 = 4, b_0 = 5 \), and define the sequences \( a_{n+1} = \frac{a_n^2}{b_n} \) and \( b_{n+1} = \frac{b_n^2}{a_n} \) for all \( n \geq 0 \). Find \( b_8 \) in the form \( \frac{5^p}{4^q} \) for integers \( p \) and \( q \).

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