
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
Alice can finish a task in 4 hours, and Bob can complete the same task in 6 hours. Alice and Bob work together on the task and also take two short breaks of 15 minutes each (half-hour total break time). Let $t$ be the total time in hours required for them to finish the task, including their breaks. Determine the equation satisfied by $t$.
A) $\left(\frac{5}{12}\right)t = 1$
B) $\left(\frac{5}{12}\right)(t-\frac{1}{2}) = 1$
C) $\left(\frac{1}{4}+\frac{1}{6}\right)(t-\frac{1}{2}) = 1$
D) $\left(\frac{1}{4}+\frac{1}{6}\right)t = 1$

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