
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 the function $$f(x)=(\log_{3} \frac {x}{27})(\log_{3}3x)$$  
(1) If $$x\in [ \frac {1}{27}, \frac {1}{9}]$$, find the maximum and minimum values of the function $f(x)$;  
(2) If the equation $f(x)+m=0$ has two roots $\alpha$ and $\beta$, find the value of $\alpha \cdot \beta$.

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