
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 \( a_1, a_2, a_3, \ldots \) is defined as follows: \( a_1 = 1 \). For \( n \geq 2 \), \( a_n \) is the smallest integer greater than \( a_{n-1} \) such that there do not exist \( 1 \leq i, j, k \leq n \) (not necessarily distinct) such that \( a_i + a_j = 3a_k \). Find \( a_{1998} \).

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