
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  $i,j$  and  $k$  are not necessarily distinct. Determine  $a_{1998}$ .

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