
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
Eliza calculates her utility from the relation $$\text{Utility} = (\text{hours of math done})^2 + (\text{hours of reading done}) \times (\text{hours of painting done}).$$ On Wednesday, she spends $t$ hours reading and $12-t$ hours painting. She spends 4 hours doing math. On Thursday, she ends up getting the same amount of utility while spending $t+1$ hours reading, $11-t$ hours painting, and $3$ hours on math. Find $t$.

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