
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 the function \( f(x)=\left\{\begin{array}{ll}
(x+1)^{2}, & x<1 \\
4-\sqrt{x-1}, & x \geqslant 1
\end{array}\right. \), determine the range of values for the independent variable such that \( f(x) \geq x \).

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