
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
Suppose $T$ is a finite set of positive integers. If the greatest integer in $T$ is removed from $T$, then 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 becomes $50$. If the greatest integer is then returned to the set, the average value of the integers now becomes $55$. The greatest integer in the original set $T$ is $90$ greater than the least integer in $T$. What is the average value of all the integers in the set $T$?
A) 48.5
B) 49.0
C) 49.5
D) 50.0
E) 50.5

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