
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
Nonzero real numbers \( x \), \( y \), \( a \), and \( b \) satisfy \( x < a \) and \( y < b \) with \( x \) and \( y \) negative, and \( a \) and \( b \) positive. How many of the following inequalities must be true?
(I) \( x+y < a+b \)
(II) \( x-y < a-b \)
(III) \( xy < ab \)
(IV) \( \frac{x+y}{x-y} < \frac{a+b}{a-b} \)
A) 0
B) 1
C) 2
D) 3
E) 4

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