
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 \( f(x) \) satisfying \( f(m+n) = f(m) f(n) \) and \( f(1) = 3 \), find the value of the expression
\[
\frac{f^{2}(1) + f(2)}{f(1)} + \frac{f^{2}(2) + f(4)}{f(3)} + \frac{f^{2}(3) + f(6)}{f(5)} + \frac{f^{2}(4) + f(8)}{f(7)}.
\]

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