
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 an even function $f(x)$ with a domain of $R$ that satisfies: for any $x_{1}$, $x_{2}\in \left[0,+\infty \right)$, $x_{1}\neq x_{2}$, $(x_{1}-x_{2})[f(x_{1})-f(x_{2})] \gt 0$. If $f(m+1)\geq f(2)$, determine the range of values for $m$.

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