
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 $y=f(x)$ includes the points $(0,4),$ $(1,2),$ and $(2,0)$.

Based only on this information, determine two points that must be on the graph of $y=f(f(x))$. If we call these points $(a,b)$ and $(c,d),$ calculate the value of $ab+cd$.

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