
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
Define the sequence  $(a_n)_{n=1}^\infty$  of positive integers by  $a_1=1$  and the condition that  $a_{n+1}$  is the least integer such that \[\mathrm{lcm}(a_1, a_2, \ldots, a_{n+1})>\mathrm{lcm}(a_1, a_2, \ldots, a_n)\mbox{.}\]
Determine the set of elements of  $(a_n)$ .

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