
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 the function $g(x) = \frac{a(x+h) + b}{c(x+h) + d}$, where $abcd \neq 0$ and $h$ is a real number. Assume $g(g(x)) = x$ for all $x$ within $g$'s domain. What are the values of $a + d - 2ch$?

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