
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
Amy writes down four integers \(a > b > c > d\) whose sum is 50. The pairwise positive differences of these numbers are \(2, 3, 4, 5, 7,\) and \(10\). What is the sum of the possible values for \(a\)?

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