
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  $E$  denote the set of all natural numbers  $n$  such that  $3 < n < 100$  and the set  $\{ 1, 2, 3, \ldots , n\}$  can be partitioned in to  $3$  subsets with equal sums. Find the number of elements of  $E$ .

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