
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 function $f(x)= \sqrt {-x^{2}+bx+c}$ with domain $D$, and for any $x$ in $D$, the condition $f(-1)\leqslant f(x)\leqslant f(1)$ holds, find the value of $b \cdot c + f(3)$.
Options:
A) $6$
B) $0$
C) $5$
D) None of the above answers are correct

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