
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 $f(x) = 2^{x} - a \cdot 2^{-x}$ defined on $\mathbb{R}$ is an odd function.

(1) Find the value of $a$ and determine the monotonicity of $f(x)$ (without providing proof);

(2) $t$ is a real number, and $f(x - t) + f(x^{2} - t^{2}) \geqslant 0$ holds for all real numbers $x$, find the value of $t$.

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