
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 \( c_0 = 3, \) \( d_0 = 4, \) and
\[
c_{n+1} = \frac{c_n^3}{d_n^2}, \quad d_{n+1} = \frac{d_n^3}{c_n^2}
\]
for all \( n \geq 0 \). Then \( d_8 = \frac{4^p}{3^q} \) for some integers \( p \) and \( q \). Find the ordered pair \( (p, q) \).

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