
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 the functions $$f(x)=x^{2}-1$$ and $$g(x)= \begin{cases} x-1, & \text{if } x>0 \\ 2-x, & \text{if } x<0\end{cases},$$
(1) Calculate the values of $f(g(2))$, $g(f(2))$, and $g(g(g(-2)))$.
(2) Find the explicit formulas for $f(g(x))$ and $g(f(x))$.

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