
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
A function \(f: \mathbb{R} \rightarrow \mathbb{R}\) satisfies
$$
f(x)+f(y)=f(x)f(y)+1-\frac{4}{xy}
$$
for all nonzero real numbers \(x\) and \(y\). Given that \(f(1)>0\), find the value of \(f(4)\).

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