
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 the interval $[-1, 1]$ and $f(1) = 1$, and $f(x)$ satisfies for any $m, n \in [-1, 1]$, we have $$\frac{f(m) + f(n)}{m + n} > 0.$$  
(1) Solve the inequality $f\left(x + \frac{1}{2}\right) + f(x - 1) < 0$;  
(2) If $f(x) \leq t^2 - 2at + 1$ holds for all $x \in [-1, 1]$ and $a \in [-1, 1]$, find the range of the real number $t$;  
(3) If $f(x) \leq t^2 - 2at + 2$ holds for all $x \in [-1, 1]$ and $t \in [-1, 1]$, find the range of the real number $a$.

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