
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 any positive integer  $n>1$ , let  $p(n)$  be the greatest prime factor of  $n$ . Find all the triplets of distinct positive integers  $(x,y,z)$  which satisfy the following properties:  $x,y$  and  $z$  form an arithmetic progression, and  $p(xyz)\leq 3.$ 

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