
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 $y=x^{2}+bx+3$ (where $b$ is a real number), the range of $y$ is $\left[0,+\infty \right)$, and the solution set of the inequality $x^{2}+bx+3 \lt c$ is $m-8 \lt x \lt m$, determine the value of the real number $c$.

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