
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 $f(x) = 2x - 4$ and $g(x) = -x + 4$.
(1) Find the values of $f(1)$, $g(1)$, and $f(1) \cdot g(1)$;
(2) Determine the explicit formula for the function $y = f(x) \cdot g(x)$, and find its zeros;
(3) Identify the intervals where the function $y = f(x) \cdot g(x)$ is monotonically increasing or decreasing.

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