
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 the function $y=f(x)$ includes the points $(2, 6)$, $(3, 4)$, and $(4, 2)$. Assuming the graph of $y=g(x)$ includes the points $(2,4)$, $(3,2)$, and $(5,6)$, determine the two points that must be on the graph of $y=g(f(x))$. If we let these points be $(a,b)$ and $(c,d)$, what is $ab+cd$?

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