
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
Given that $a_1$ and $a_2$ are real numbers such that $a_1 \neq a_2$ and $5a_i^2 + ka_i - 2 = 0$ for $i = 1, 2$, find $a_1 + a_2$.
A) $\frac{k}{5}$
B) $-\frac{k}{5}$
C) $-\frac{k}{2}$
D) $\frac{k}{2}$

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