
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 that function $f(x)$ is a direct proportional function, and function $g(x)$ is an inverse proportional function, with $f(1) = 1$ and $g(1) = 2$.

1. Find functions $f(x)$ and $g(x)$;
2. Determine the odd or even property of function $f(x) + g(x)$;
3. Find the minimum value of function $f(x) + g(x)$ on the interval $(0, \sqrt{2}]$.

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