
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 \(a\), \(b\), \(c\), and \(d\) are positive integers, and
\[
\log_{a} b=\frac{3}{2}, \quad \log_{c} d=\frac{5}{4}, \quad \text{and} \quad a-c=9,
\]
find the value of \(a + b + c + d\).

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