
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 quadratic function $f(x)=ax^{2}-2x+c$, where $x\in \mathbb{R}$, with a range of $[0,+\infty)$, determine the maximum value of $\frac{1}{c+1} + \frac{4}{a+4}$.
A) $\frac{3}{2}$
B) $\frac{4}{3}$
C) $\frac{5}{4}$
D) $\frac{6}{5}$

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