
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
Consider the set  $$ \mathcal{S}=\{(a, b, c, d, e): 0<a<b<c<d<e<100\} $$  where  $a, b, c, d, e$  are integers. If  $D$  is the average value of the fourth element of such a tuple in the set, taken over all the elements of  $\mathcal{S}$ , find the largest integer less than or equal to  $D$ .

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