
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
Three pumpkins are weighed two at a time in all possible ways, and the weights of the pairs are 12 kg, 13 kg, and 15 kg. Let's denote the weights of the pumpkins as a, b, and c. Express the weights of the pairs in terms of a, b, and c.

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