
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 functions
$$
f(x)=x^{2}-2x, \quad g(x)=\left\{\begin{array}{ll}
x-2, & x \geqslant 1, \\
-x, & x<1.
\end{array}\right.
$$

find the solution set of the inequality $f(x) \leqslant 3g(x)$.

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