
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

16. Arrange the numbers that can be expressed as the sum of $m$ $(m>1)$ consecutive positive integers in ascending order to form a sequence. This sequence is denoted as $\{a(m, n)\}$, where $a(m, n)$ represents the $n$-th smallest number that can be expressed as the sum of $m$ consecutive positive integers.
(1) Write out $a(2,1), a(2,2), a(2,3), a(2,4)$;
(2) Find the explicit formula for $a(m, n)$;
(3) Can 2000 be expressed as the sum of several consecutive positive integers? If so, find all such solutions; if not, explain why.

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