
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
Solve the inequality

\[ f(g(x)) > g(f(x)) \]

where 

\[ f(x) = \left\{
\begin{array}{cc}
x, & x \geq 0 \\
0, & x < 0
\end{array}
\right.,
\quad
g(x) = \left\{
\begin{array}{cc}
2-x, & x < 2 \\
0, & x \geq 2
\end{array}
\right.
\]

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