
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
Alpha, Beta, and Gamma, working together, complete a task in 4 hours less than Alpha alone, 2 hours less than Beta alone, and in two-thirds of the time required by Gamma alone. Let $t$ be the number of hours Alpha and Beta need to complete the task together. Find the value of $t$.

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