
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
The sequence of positive integers  $\{a_n, n\ge 1\}$  is such that  $a_n\le a_{n+1}\le a_n+5$  and  $a_n$  is divisible by  $n$  for all  $n \ge 1$ . What are the possible values of  $a_1$ ?

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