
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
Consider a new function $g(x) = \frac{2ax - b}{cx - 2d}$, where $a, b, c, d \neq 0$ and $g(g(x)) = x$ for all $x$ in the domain of $g$. Assume further that $b=3a$ and $c=3d$. What is the value of $2a - 2d$?

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