
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 $u$ and $v$, then $u \, \oplus \, v$ is a positive real number defined in terms of $u$ and $v$ by some fixed rule. Suppose the operation $u \, \oplus \, v$ satisfies the equations $(uv) \, \oplus \, v = u(v \, \oplus \, v)$ and $(u \, \oplus \, 1) \, \oplus \, u = u \, \oplus \, 1$ for all $u,v>0$. Additionally, it is known that $2 \, \oplus \, 2 = 1$. Find $37 \, \oplus \, 5$.

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