
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
Georgina, Hugo, and Isla paint a fence comprised of exactly 60 pickets.
Georgina starts with the first picket and paints every $g$ th picket;
Hugo starts with the third picket and paints every $h$ th picket; and
Isla starts with the second picket and paints every $i$ th picket.
Call a number $100g+10h+i$ decorative when the triple $(g,h,i)$ of positive integers results in every picket being painted exactly once. Find the sum of all the decorative integers.

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