
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
The sum of the integers at the vertices of a square is the product of the integers on two adjacent edges, plus the product of the integers on the two other adjacent edges, plus the product of the integers on the two other adjacent edges, plus the product of the integers on the two other adjacent edges. If the sum of the integers at the vertices is 15, determine the sum of the integers on the edges of the square.

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