
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
Two positive numbers $x$ and $y$ are in the ratio $a:(b+1)$ where $0 < a < b+1$. If $x+y = c$ and $x - y = d$ find the smaller of $x$ and $y$.
A) $\frac{ac}{a+b}$  
B) $\frac{(b+1)c}{a+b+1}$  
C) $\frac{ac}{a+b+1}$  
D) $\frac{(b+1)c}{a+b}$

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