
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 $a:b$ where $0 < a < b$. The sum of these numbers is updated, such that together they sum up to $c-d$, where $d = 2x - y$ and $0 < d < c$. Compute the smaller of $x$ and $y$.
A) $\frac{2ac - bc}{3(2a-b)}$
B) $\frac{2ac - bc}{2a-b}$
C) $\frac{3c}{2a-b}$
D) $\frac{bc}{a+b}$ 
E) $\frac{2ac - bc}{a+b}$

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