
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
Suppose the graph of $y=g(x)$ includes the points $(1,4),$ $(2,6),$ and $(3,2)$, and $(4,1)$.

Based only on this information, there are three points that must be on the graph of $y=g(g(x))$. If we call those points $(a,b)$, $(c,d)$, and $(e,f)$, what is $ab+cd+ef$?

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