
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

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

if 

\[ f(x) = \begin{cases} 
   x, & \text{if } x \geq 0  \\
   0, & \text{if } x < 0 
\end{cases}, 
\; g(x) = \begin{cases} 
   2 - x, & \text{if } x < 2  \\
   0, & \text{if } x \geq 2 
\end{cases}.
\]

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