
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 $f(x) = x^2 + ax + b$ ($a, b \in \mathbb{R}$) has a range of $[0, +\infty)$, if the solution set of the inequality $f(x) < c$ is $(m, m+8)$, then the value of the real number $c$ is \_\_\_\_\_\_.

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