
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
The real numbers $c, b, a$ form an arithmetic sequence. The quadratic equation $ax^2+bx+c=0$ has exactly one root. Given that $a = 5, c = 1$, find this root. Assume $b, a, c \geq 0$.
A) $-\frac{1}{5}$
B) $-\frac{\sqrt{5}}{5}$
C) $-\frac{2\sqrt{5}}{5}$
D) $-\frac{3\sqrt{5}}{5}$

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