
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
Let a constant \( a \in \mathbf{R} \) and the function
\[ f(x) = (a - x)|x| \]

have an inverse function \( f^{-1}(x) \). If the inequality
\[ f^{-1}\left(x^{2} + m\right) < f(x) \]

holds for all \( x \in [-2,2] \), find the range of values for the real number \( m \).

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