
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
Consider the function $y = F(x)$ defined by $F(x) = \lfloor \sqrt{|x+2|} \rfloor + \left\lceil \frac{8}{\pi} \cdot \text{atan}(\sqrt{|x|}) \right\rceil$.

What is the value of $F(4)$?

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