
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
For each positive integer  $ n$  find all positive integers  $ m$  for which there exist positive integers  $ x_1<x_2<...<x_n$  with:

 $ \frac{1}{x_1}\plus{}\frac{2}{x_2}\plus{}...\plus{}\frac{n}{x_n}\equal{}m.$ 

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