
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 functions $f\left(x\right)$ and $g\left(x\right)$ are provided in the table below:

| $x$ | $1$ | $2$ | $3$ |
|-----|-----|-----|-----|
| $f\left(x\right)$ | $1$ | $3$ | $1$ |
| $g\left(x\right)$ | $3$ | $2$ | $1$ |

Find the value of $f\left[g\left(1\right)\right]$ as _______; then determine the solution set of the inequality $f\left[g\left(x\right)\right] \gt g\left[f\left(x\right)\right]$ as _______.

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