
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

In the following pairs of integer triplets I-IV, the sum and the sum of the squares of the three numbers in each triplet are equal:

| I | 38, 108, 268 | 8, 168, 238 |
| II | 30007, 207, 60407 | 7, 60207, 30407 |
| III | 4, 500, 405 | 5, 400, 504 |
| IV | 6, 350, 164 | 14, 150, 356 |

Find any patterns in their formation, and based on these, provide general procedures to form such pairs of triplets.

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