
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
Hermione has a utility function based on the hours of potions done and the hours of reading spells. On Wednesday, she dedicates $h$ hours to reading spells and spends $10 - h$ hours on potions. On Thursday, she manages to achieve the same utility while spending $4-h$ hours reading spells and $h+2$ hours doing potions. Find $h$, represented as a fraction in lowest terms.

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