
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 integers $a$ and $b$, define the operation $a \, \otimes \, b$ which satisfies $(a^2 b) \, \otimes \, b = a(b \, \otimes \, b)$ and $(a \, \otimes \, 1) \, \otimes \, a = a \, \otimes \, 1$ for all $a, b > 0$. Knowing that $1 \, \otimes \, 1 = 1$, determine the value of $5 \, \otimes \, 18$.

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