
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
In the given triangle, for $\angle A$ to be the largest angle of the triangle, it must satisfy certain conditions based on the side lengths. The sides of the triangle are labeled as follows: $AB = y+6$, $AC = y+3$, and $BC = 2y$. What is the least possible value of $\text{max}(y+6, y+3) - \text{min}(y+6, y+3)$, expressed as a common fraction?

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