
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
Arrange the positive integers into the following pattern:
```
1
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16
...
```
If the number located in the $i$-th row and $j$-th column is denoted as $a_i^j$, then the number 2005 in the table should be expressed as $a_i^j$.

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