
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 functions $f(x)=2x-4$, $g(x)=-x+4$.

  (1) Find the values of $f(1)$ and $g(1)$;  
(2) Find the explicit formula for the function $y= f(x) g(x)$, and find the zeros of this function;  
(3) Describe the intervals of monotonicity for the function $y= f(x) g(x)$.

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