
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
Two boys together have at least seven dozen and no more than eight dozen nuts. If the first boy gave the second boy a quarter of his nuts, and then the second boy gave the first boy a fifth of all the nuts he had at that point, the first boy would end up with one more nut than he initially had. How many nuts does each boy have?

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