
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
Charlie and Dana start working on the same day. Charlie works for 4 days and then takes 2 days off, while Dana works for 6 days and takes 1 day off. Over the first 1500 days, calculate the number of days when both Charlie and Dana have off-days on the same day.

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