
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  $T = \{ 1, 2, 3, \dots, 14, 15 \}$ .  Say that a subset  $S$  of  $T$  is *handy* if the sum of all the elements of  $S$  is a multiple of  $5$ .  For example, the empty set is handy (because its sum is 0) and  $T$  itself is handy (because its sum is 120).  Compute the number of handy subsets of  $T$ .

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