
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 \( 0 \leq a_0 < a_1 < a_2 < \ldots \) is such that every non-negative integer can be uniquely expressed as \( a_i + 2a_j + 4a_k \) (where \( i, j, k \) are not necessarily distinct). Find \( a_{1998} \).

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