
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. Removing the largest integer from $T$ results in the remaining integers having an average of 45. If the smallest integer is also removed, then the average of the remaining integers drops to 40. If the largest integer is then reintroduced to the set, the average rises to 50. The largest integer in the set $T$ exceeds the smallest integer by 90. Determine the average value of all integers in the set $T$.
A) 52.8
B) 53.4
C) 54.0
D) 54.6

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