
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
Suppose there exists an arithmetic operation $\circ$ defined for any two positive real numbers $a$ and $b$ such that it follows the rules $(a^2 b) \circ b = a(b \circ b)$ and $(a \circ 1) \circ a = a \circ 1$ for all $a,b>0$. Given that $1 \circ 1 = 1$, find $15 \circ 7$.

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