
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
For a function $f(x)$ defined on the interval $[0,1]$ that satisfies the following two conditions, we call it a G-function:
1. For any $x \in [0,1]$, $f(x) \geq 0$;
2. For $x_1 \geq 0, x_2 \geq 0, x_1 + x_2 \leq 1$, it holds that $f(x_1+x_2) \geq f(x_1) + f(x_2)$. Given the functions $g(x)=x^2$ and $h(x) = 2^x - b$, both defined on $[0,1]$:
   1. Is $g(x)$ a G-function? Explain your reasoning.
   2. If $h(x)$ is a G-function, determine the set of real numbers $b$.

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