
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 $$\text{Utility} = 2 \times (\text{hours of math done}) \times (\text{hours of frisbee played}).$$ On a particular Wednesday, he plays $s$ hours of frisbee and spends $10 - 2s$ hours doing math. On Thursday, to achieve the same utility as Wednesday, he spends $3 - s$ hours playing frisbee and $2s + 4$ hours on math. Find $s$. Answer as a fraction in lowest terms.

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