
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 that the domain of functions $f(x)$ and $g(x)$ is $\{1, 2, 3\}$, and it satisfies $f(1)=f(3)=1$, $f(2)=3$, $g(x)+x=4$, find the value(s) of $x$ for which $f[g(x)]>g[f(x)]$.

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