
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 $(a \star b) \star b = a(b \star b)$ and $(a \star 1) \star a = a \star 1$ for all $a, b > 0$. Moreover, $1 \star 1 = 2$. Find $5 \star 10$.

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