
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
Seven pirates were dividing five identical treasure chests. They agreed that five of them would take one chest each, while the remaining two would receive fair compensation equal to the value of a chest. Each recipient of a chest paid 10,000 doubloons into a common fund, which was then distributed among the remaining pirates. What was the assessed value of one chest?

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