
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 $f(x)=\left\{{\begin{array}{l}{{x^2}-m({2x-1})+{m^2},x≤2,}\\{{2^{x+1}},x＞2,}\end{array}}\right.$ find the range of $m$ such that $f(x)$ reaches its minimum value when $x=2$.

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