
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
Let \( f(x) = \begin{cases}
x^2, & \text{if } |x| \geqslant 1, \\
kx, & \text{if } |x| < 1 
\end{cases} \) and \( g(x) \) be a quadratic function. If the range of \( f(g(x)) \) is \([0, +\infty)\), determine the range of the real number \( k \).

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