
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
A function $f(x)$ defined on the interval $[0, 1]$ and satisfying the following two conditions is called an inequality function:
1. For any $x \in [0, 1]$, it always holds that $f(x) \geq 0$;
2. When $x_1 \geq 0$, $x_2 \geq 0$, and $x_1 + x_2 \leq 1$, it always holds that $f(x_1 + x_2) \geq f(x_1) + f(x_2)$.

Given that the functions $g(x) = x^3$ and $h(x) = 2^x - a$ are defined on $[0, 1]$.
1. Is the function $g(x)$ an inequality function? Please explain your reasoning.
2. If the function $h(x)$ is an inequality function, find the set of real numbers $a$.

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