
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
Five distinct points are arranged on a plane so that the segments connecting them have lengths $a$, $a$, $a$, $2a$, $x$, and $3a$. What is the ratio of $x$ to $a$?
**A)** $\frac{\sqrt{3}}{3}$ 
**B)** $\frac{\sqrt{3}}{2}$
**C)** $\frac{\sqrt{2}}{3}$
**D)** $\frac{3\sqrt{3}}{2}$
**E)** $\pi$

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