
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 \( (3,2) \).

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

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