
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
A set $\mathcal{T}$ of distinct positive integers has the following property: for every integer $y$ in $\mathcal{T},$ the arithmetic mean of the set of values obtained by deleting $y$ from $\mathcal{T}$ is an integer. Given that 1 belongs to $\mathcal{T}$ and that 1989 is the largest element of $\mathcal{T},$ what is the greatest number of elements $\mathcal{T}$ can have?

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