
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
The value range of the function $f(x) = \begin{cases} 2x^{2} & (0 \leq x < 1) \\ 2 & (1 \leq x < 2) \\ 3 & (x \geq 2)\end{cases}$, calculate the interval representing all possible output values of $f(x)$.

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