
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
Let \( f(x) = x^2 + px + q \). It is known that the inequality \( |f(x)| > \frac{1}{2} \) has no solutions on the interval \([2, 4]\). Find \( \underbrace{f(f(\ldots f}_{2017}\left(\frac{5-\sqrt{11}}{2}\right)) \ldots) \). Round your answer to the nearest hundredth if necessary.

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