
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
Given that the total amount paid for the students' work was $1,470, and that students from Apex school worked for 4 weekdays and 2 weekend days, students from Beacon school worked for 6 weekdays and 1 weekend day, and students from Citadel school worked for 8 weekdays and 3 weekend days, with each student receiving the same amount for a weekday's work and double the amount for weekend work, determine the total amount earned by the students from Beacon school.

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