
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 two functions y=f(x) and y=g(x) with their respective domains D_f and D_g, a function h(x) is defined as follows:
$$h(x)= \begin{cases} f(x)g(x),\text{when }x∈D_{f}\text{ and }x∈D_{g} \\ f(x),\text{when }x∈D_{f}\text{ and }x∉D_{g} \\ g(x),\text{when }x∉D_{f}\text{ and }x∈D_{g}\end{cases}$$
If f(x) = x-2 (x ∈ R) and g(x) = -2x+3 (x ≥ 1), find the range of the function h(x).

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