
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 $f(x) =$ 
$$
\begin{cases} 
f(4-x), & x > -2 \\
2^{-x}, & x \leq -2
\end{cases}
$$
which is increasing on the interval $[2, +\infty)$, and $f(0) = 0$, find the minimum value of $f(x)$.

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