
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's modify the problem slightly. Sara writes down four integers $a > b > c > d$ whose sum is $52$. The pairwise positive differences of these numbers are $2, 3, 5, 6, 8,$ and $11$. What is the sum of the possible values for $a$?

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