
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 $f(x) = \dfrac {2^{x}-a\cdot 2^{-x}}{2^{x}+2^{-x}}$ is an odd function defined on $\mathbb{R}$,  
(1) Find the value of the real number $a$ and the range of the function $f(x)$;  
(2) Let $g(x) = (2^{x}+2^{-x}) \cdot f(x)$,  
(i) Determine the monotonicity of the function $y=g(x)$ (no need to justify the reason), and find the range of the real number $t$ such that the inequality $g(x^{2}+tx)+g(4-x) > 0$ holds for all $x \in \mathbb{R}$;  
(ii) Let $h(x)=2^{2x}+2^{-2x}-2m \cdot g(x)$, and suppose $h(x)$ has a minimum value of $-2$ on $[1,+\infty)$. Find the value of the real number $m$.

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