
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
A certain scientific research unit intends to allocate a certain amount of funding to reward its researchers. The person who comes in first place receives more than half of the total funds by ¥10,000, the second place receives more than half of the remaining funds by ¥10,000, and so on, following the same rule. By the time it comes to the tenth place, the funds are distributed exactly. How much funding, in tens of thousands of yuan, did this scientific research unit offer for rewards?

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