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

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