
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 a function $f(x)$ with domain $\mathbb{R}$ satisfying $f(x+2)=\frac{f(x)}{2}$, and $f(x)=|x|-1$ for $x\in[-1,1]$, find the minimum value of $f(x)$ when $x \in [-6,-4]$.

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