
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
Given that \( a, b, c, d \) are all positive integers, and \( \log_a b = \frac{3}{2} \), \( \log_c d = \frac{5}{4} \), if \( a - c = 9 \), then what is \( b - d \)?

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