
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
Ethan derives utility according to the relation $$\text{Utility} = 2 \times (\text{hours of coding done}) \times (\text{hours of swimming}) + 1.$$ On Saturday, he swims for $t$ hours and spends $10 - 2t$ hours coding. On Sunday, he gains the same utility while spending $4 - t$ hours swimming and $2t + 2$ hours coding. Find $t$ as a fraction.

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