
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
The functions $f(x)$ and $g(x)$ satisfy the following conditions for all positive real numbers $x$ and $y$:
\[f(xy) = \frac{f(x)}{y},\]
\[g(x + y) = g(x) + g(y).\]
If $f(15) = 10$ and $g(5) = 3$, find $f(45)$ and $g(10)$.

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