
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
Given the function $y=f(x)$ which passes through the points $(1,3), (2,1),$ and $(3,5)$, find two points that must be on the graph of $y = f(f(x))$. Let's denote these points as $(a, b)$ and $(c, d)$. Calculate $ab + cd$.

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