
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 four positive integers \(a, b, c, d\) satisfy \(a < b < c < d\). When the sums of the six pairs of these integers are calculated, the six answers are all different and the four smallest sums are 6, 8, 12, and 21. What is the value of \(d\)?

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