
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 \( f(x) \) is an odd function defined on \([-1,1]\) with \( f(1) = 1 \), and for \( a, b \in [-1,1] \) with \( a + b \neq 0 \), it holds that \( \frac{f(a) + f(b)}{a + b} > 0 \). If the inequality
\[ f(x) \leqslant m^{2} - 2 a m + 1 \]
is satisfied for all \( x \in [-1,1] \) and \( a \in [-1,1] \), find the range of values for the real number \( m \).

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