
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
Carlos and Dana start their new jobs on the same day. Carlos's schedule is 5 work-days followed by 2 rest-days. Dana's schedule is 9 work-days followed by 4 rest-days. On how many of their first 1500 days do both have rest-days on the same day.

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