
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
Grace can paint a room in 6 hours, Henry can paint the room in 8 hours, and Julia can paint it in 12 hours. They decide to paint the room together but take different breaks; Grace and Henry take a one-hour break, while Julia takes a two-hour break. Let $t$ be the total time, in hours, required for them to complete the job working together, including their breaks. What is the expression that $t$ must satisfy?

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