
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 that for any $m$, $n\in[-1,1]$, there is $\frac{f(m)+f(n)}{m+n} > 0$.
(1) Solve the inequality $f(x+ \frac{1}{2})+f(x-1) < 0$;
(2) If $f(x)\leqslant t^{2}-2at+1$ holds for all $x\in[-1,1]$, $a\in[-1,1]$, find the range of values of the real number $t$;
(3) If $f(x)\leqslant t^{2}-2at+2$ holds for all $x\in[-1,1]$, $t\in[-1,1]$, find the range of values of the real number $a$.

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