
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
Let $x \, \star \, y$ be a positive real number defined for any two positive real numbers $x$ and $y$. Suppose the operation $x \, \star \, y$ satisfies the equations $(x^2y) \, \star \, y = x(y \, \star \, y)$ and $(x \, \star \, 2) \, \star \, x = x \, \star \, 2$ for all $x, y > 0$. Given that $2 \, \star \, 2 = 2$, find $12 \, \star \, 49$.

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