
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 the function \( f(x) = \frac{2ax - b}{3cx + d} \) where \( b, d \neq 0 \) and \( abcd \neq 0 \), assume \( f(f(x)) = x \) holds true for all \( x \) in the domain of \( f \). What is the value of \( 3a - 2d \)?

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