
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
In the existing rules of arithmetic for real numbers, we introduce a new operation "⊕": When $a \geq b$, $a ⊕ b = a$; when $a < b$, $a ⊕ b = b^2$. The function $f(x) = (1 ⊕ x) \cdot x$ (where “$\cdot$” stands for the usual multiplication) is defined. Find the range of the function $f(x)$ on the interval $[0, 2]$.

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