
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 for every $ x,y\in \Re ^{\plus{}}$ the function  $ f: \Re ^{\plus{}} \to \Re$  satisfies the condition  $ f\left(x\right)+f\left(y\right)=f\left(x\right)f\left(y\right)+1-\frac{1}{xy}$, if  $ f\left(2\right)<1$, calculate $ f\left(3\right)$.

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