
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
A rectangle \( P Q R S \) has side-lengths \( a \) and \( b \), with \( a < b \). The rectangle \( P T U V \) has side-lengths \( c \) and \( d \), with \( c < d \). Also, \( a < d \) and \( c < b \), as shown. The sides \( R S \) and \( T U \) cross at \( X \). Which of these conditions guarantees that \( Q, X \), and \( V \) lie on a straight line?
A) \(\frac{a}{b}+\frac{c}{d}=1\)
B) \(\frac{a}{c}+\frac{b}{d}=1\)
C) \(\frac{a}{d}+\frac{c}{b}=1\)
D) \(\frac{a}{c}+\frac{d}{b}=1\)
E) \(\frac{c}{a}+\frac{b}{d}=1\)

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