
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 set  $\mathcal{A}$  be a 90-element subset of  $\{1,2,3,\ldots,100\},$  and let  $S$  be the sum of the elements of  $\mathcal{A}$ .  Find the number of possible values of  $S$ .

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