
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 $f(x) \geq 2$ always holds, and the range of real number $a$ is $\{a|a \leq -5 \text{ or } a \geq 5\}$, then the set of all possible values of $m$ is \_\_\_\_\_\_.

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