
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
\[a_{n + 1} = \frac{a_n^3}{b_n} \quad \text{and} \quad b_{n + 1} = \frac{b_n^3}{a_n}\]for all $n \ge 0.$  Calculate $b_6$ in the form $\frac{5^p}{3^q}$ where $p$ and $q$ are integers.

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