
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 $f(x)$ such that for any real number $x$, $f(x) = kf(x + 2)$, where $k$ is a negative constant, and $f(x)$ has the expression $f(x) = x(x - 2)$ in the interval $[0, 2]$.

1. Find the values of $f(-1)$ and $f(2.5)$;
2. Write out the expression of $f(x)$ in the interval $[-3, 3]$ and discuss the monotonicity of the function $f(x)$ in $[-3, 3]$;
3. Find the minimum and maximum values of $f(x)$ in $[-3, 3]$ and find the corresponding values of the independent variable.

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