
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 that the function $f(x)$ defined on $R$ is monotonically increasing on $\left[-2,+\infty \right)$, and $f(x-2)$ is an even function, determine the range of values of $x$ that satisfy $f(2x) < f(x+2)$.

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