
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
A positive integer is **superb** if it is the least common multiple of  $1,2,\ldots, n$  for some positive integer  $n$ .
Find all superb  $x,y,z$  such that  $x+y=z$ .
*Proposed by usjl*

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