
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 scientific research institute wishes to allocate a certain amount of funds as a reward for its researchers. The first place gets more than half of the total funds by 10,000 Yuan; the second place gets more than half of the remaining funds by 10,000 Yuan; this pattern continues in the same way, with each subsequent place receiving more than half of the remaining funds by 10,000 Yuan, until the 10th place gets the last of the funds. Calculate the total amount of funds in ten-thousand Yuan that this research institute has allocated for the rewards.

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