
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
Let  $A$  be a set of natural numbers, for which for  $\forall n\in \mathbb{N}$  exactly one of the numbers  $n$ ,  $2n$ , and  $3n$  is an element of  $A$ . If  $2\in A$ , show whether  $13824\in A$ .

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