
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
Five boys bought a video game system for $\textdollar 120$. The first boy paid one third of the sum of the amounts paid by the other four boys; the second boy paid one fourth of the sum of the amounts paid by the other four boys; the third boy paid one-fifth of the sum of the amounts paid by the other four boys, and the fourth boy paid $\textdollar 20$. Calculate the amount paid by the fifth boy.

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