
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 \(a_{0}, a_{1}, a_{2}, \ldots\) be an increasing sequence of nonnegative integers such that every nonnegative integer can be expressed uniquely in the form \(a_{i} + 2a_{j} + 4a_{k}\), where \(i, j, k\) are not necessarily distinct. Determine \(a_{1998}\).

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