
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 $f(x)= \begin{cases} \overset{x^{2},x\geqslant 0}{-x^{2},x < 0} \end{cases}$, if for any $x\geqslant 1$ there is $f(x+2m)+mf(x) > 0$ always holds true, then the range of the real number $m$ is _____ .

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