
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
Four distinct points are arranged on a plane such that the segments connecting them have lengths $a$, $a$, $a$, $b$, $b$, and $c$. Determine the ratio of $c$ to $a$.
A) $\frac{1}{2}$
B) $\frac{\sqrt{3}}{2}$
C) $\sqrt{2}$
D) $1$

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