
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 sequence of integers  $ a_{1},a_{2},a_{3},\ldots$  is defined as follows:  $ a_{1} \equal{} 1$  and for  $ n\geq 1$ ,  $ a_{n \plus{} 1}$  is the smallest integer greater than  $ a_{n}$  such that  $ a_{i} \plus{} a_{j}\neq 3a_{k}$  for any  $ i,j$  and  $ k$  in  $ \{1,2,3,\ldots ,n \plus{} 1\}$ , not necessarily distinct. Determine  $ a_{1998}$ .

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