
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 \( T \) be a finite set of positive integers. The greatest integer in \( T \) is removed from \( T \), and the average value of the integers remaining is \( 45 \). If the least integer in \( T \) is also removed, then the average value of the integers remaining is \( 50 \). If the greatest integer is returned to the set, the average value of the remaining integers becomes \( 55 \). The greatest integer in \( T \) is \( 50 \) greater than the least integer in \( T \). Find the average value of all the integers in the set \( T \).
A) 45
B) 47
C) 50
D) 52
E) 55

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