
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 a function $f(x)=x^{2}+ax+b$ ($a,b \in \mathbb{R}$) with its domain being $\mathbb{R}$ and its range being $[0,+\infty)$, if the solution set of the inequality $f(x) < c$ is $(1,7)$, then the value of the real number $c$ is \_\_\_\_\_\_.

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