
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
Students from three different schools worked on a summer project. Six students from Atlas school worked for $4$ days, five students from Beacon school worked for $6$ days, and three students from Cedar school worked for $10$ days. The total payment for the students' work was $774. Given that each student received the same amount for a day's work, determine how much the students from Cedar school earned altogether.

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