
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
Consider four integers \( a > b > c > d \) such that their sum is \( 48 \) and the pairwise positive differences are \( 2, 4, 5, 7, 8, \) and \( 11 \). Determine the sum of all possible values for \( a \).

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