
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 Doug can paint a room in 6 hours, Dave can paint the same room in 8 hours, and Ralph can paint the room in 12 hours, and they take a break of 90 minutes for lunch, derive the equation to find the total time, in hours, required for them to complete the painting of the room, including their break.

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