
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
Given any two positive real numbers $a$ and $b$, then $a \, \star \, b$ is a positive real number defined in terms of $a$ and $b$ by some fixed rule. Suppose the operation $a \, \star \, b$ satisfies the equations $(ab) \, \star \, b = a(b \, \star \, b)$ and $(a \, \star \, 1) \, \star \, a = a \, \star \, 1$ for all $a, b > 0$. Given that $1 \, \star \, 1 = 2$, find $24 \, \star \, 75$.

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