
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
An employee's pension increases according to the square root of their years of service. If the employee had worked $c$ years more, their pension would have increased by $r$ dollars. If they instead worked $d$ years more $(d \neq c)$, their pension would have increased by $s$ dollars more than the original annual pension. Determine his annual pension in terms of $c, d, r$, and $s$.
A) $\frac{(r-s)^2}{2\sqrt{cd}}$
B) $\frac{cr^2 - ds^2}{2(cr - ds)}$
C) $\sqrt{(c-d)(r-s)}$
D) $\frac{cs^2 - dr^2}{2(dr - cs)}$

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