
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 nonzero real numbers $x$, $y$, $a$, $b$, $c$, and $d$ such that $x < a + c$ and $y < b + d$ where $c > 0$ and $d > 0$. How many of the following inequalities must be true?
$\textbf{(I)}\ x+y < a+b+c+d\qquad$
$\textbf{(II)}\ x-y < a+c-b-d\qquad$
$\textbf{(III)}\ xy < ab + ad + cb + cd\qquad$
$\textbf{(IV)}\ \frac{x}{y} < \frac{a+c}{b+d}$
A) 0
B) 1
C) 2
D) 3
E) 4

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