
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
Find all sets of positive integers  $A=\big\{ a_1,a_2,...a_{19}\big\}$  which satisfy the following: $1\big) a_1+a_2+...+a_{19}=2017;$  $2\big) S(a_1)=S(a_2)=...=S(a_{19})$  where  $S\big(n\big)$  denotes digit sum of number  $n$ .

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