
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 $f(x) = x^2 - bx + c$ and $f(1) = 0, f(2) = -3$,
1. Find the explicit expression of the function $f(x)$.
2. Find the explicit expression of $f\left( \frac {1}{ \sqrt {x+1}} \right)$ and its domain.

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