
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
Esteban the alchemist have  $8088$  copper pieces,  $6066$  bronze pieces,  $4044$  silver pieces and  $2022$  gold pieces. He can take two pieces of different metals and use a magic hammer to turn them into two pieces of different metals that he take and different each other. Find the largest number of gold pieces that Esteban can obtain after using the magic hammer a finite number of times. $\textbf{Note:}$  *If Esteban takes a copper and bronze pieces, then he turn them into a silver and a gold pieces.*

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