
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
(Ⅰ) Calculate: $\sqrt[3]{(-4)^3} - \left( \frac{1}{2} \right)^0 + 25^{\frac{1}{2}}$;

(Ⅱ) Given the functions $f(x)= \frac{1}{1+x}$ and $g(x)=x^2+2$, find the domain of $f(x)$ and the value of $f(g(2))$.

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