
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 $f(x)=ax^{2}-(2a+1)x+2$, where $a\in \mathbb{R}$  
(I) Solve the inequality: $f(x) > 0$  
(II) When $a > 0$, and $(x,y)$ satisfies the inequality $y\geqslant f(|x|)$, find the minimum value of $x+y$ (expressed in terms of $a$);

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