
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 monetary prize was distributed among three inventors: the first received half of the total prize minus $3 / 22$ of what the other two received together. The second received $1 / 4$ of the total prize and $1 / 56$ of the money received together by the other two. The third received 30,000 rubles. What was the total prize and how much did each inventor receive?

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