
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
Let $a, b, c, d, e$ have the values 1, 2, 3, 4, and 5, not necessarily in that order. What is the largest possible value of the sum of the five products $ab$, $bc$, $cd$, $de$, and $ea$?

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