
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  $ T \equal{} \{1,2,3,4,5,6,7,8\}$ . Find the number of all nonempty subsets  $ A$  of   $ T$  such that  $ 3|S(A)$  and  $ 5\nmid S(A)$ , where  $ S(A)$  is the sum of all the elements in  $ A$ .

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