
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 two positive real numbers $a$ and $b$, the operation $a \, \star \, b$ is defined such that it satisfies $(ab) \, \star \, b = a (b \, \star \, b)$ and $(a \, \star \, 1) \, \star \, a = a \, \star \, 1$ for all $a, b > 0$. If $1 \, \star \, 1 = 2$, find the value of $5 \, \star \, 10$.

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