
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 that the function $f(x)$ is defined on the domain $[-1,1]$, if for any $x,y \in [-1,1]$, it holds that $f(x+y)=f(x)+f(y)$, and when $x > 0$, $f(x) > 0$. Let $f(1)=1$, if $f(x) < m^2-2am+1$ for all $x \in [-1,1], a \in [-1,1]$ always holds, then the range of the real number $m$ is ______.

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