
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 a function \( f(x) \) with the domain \( \mathbf{R}^{+} \), for any positive numbers \( x_{1} \) and \( x_{2} \), the function satisfies \( f(x_{1} x_{2}) = f(x_{1}) + f(x_{2}) \). Additionally, \( f(8) = 3 \). Find the value of \( f(\sqrt{2}) \).

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