
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 $f(x)$ is an increasing function defined on $\{x|x>0\}$, and $f\left( \frac{x}{y} \right) = f(x) - f(y)$  
(1) Find the value of $f(1)$;  
(2) If $f(6)=1$, solve the inequality $f(x+3)-f\left( \frac{1}{x} \right)<2$.

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