
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 $f(x)=|x-a|+m|x+a|$ $(0 < m < 1, m, a \in \mathbb{R})$, if for any real number $x$ the inequality $f(x) \geqslant 2$ always holds, the range of real number $a$ is $\{a|a\leqslant -5$ or $a\geqslant 5\}$. Then, the set of all possible values of $m$ is \_\_\_\_\_\_.

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