
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 $f(x)= \dfrac {1}{1+x}$ ($x \in \mathbb{R}$ and $x \neq -1$), and $g(x)=x^{2}+2$ ($x \in \mathbb{R}$).
(1) Find the values of $f(2)$ and $g(2)$;
(2) Find the value of $f[g(2)]$;
(3) Find the expressions for $f[g(x)]$ and $g[f(x)]$.

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