
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
Samson derives utility according to the relation $$\text{Utility} = \text{hours of math done} \times \text{hours of frisbee played}.$$ On a certain Monday, he plays $t$ hours of frisbee and spends $10 - t$ hours doing math. On the following Tuesday, he achieves the same utility while spending $4-t$ hours playing frisbee and $t+5$ hours on math. Furthermore, on both days, the total hours spent on activities must be at least 8 hours. Find $t$ as a fraction in lowest terms.

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