
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]


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Four boys purchased a video game system for $\textdollar 80$. The first boy paid two-fifths of the sum of the amounts paid by the other boys; the second boy paid one-fourth of the sum of the amounts paid by the other boys; and the third boy paid one-sixth of the sum of the amounts paid by the other boys. Calculate the amount paid by the fourth boy.

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