
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
What is the perimeter of hexagon $ABCDEF$ where the vertices are positioned on a coordinate plane as follows:
- $A$ is at the origin $(0,0)$
- $B$ is directly to the right of $A$ at $(2,0)$
- $C$ is at $(3,\sqrt{3})$
- $D$ is at $(2,2\sqrt{3})$
- $E$ is at $(0,2\sqrt{3})$
- $F$ is back at $(-1,\sqrt{3})$
Calculate the perimeter of $ABCDEF$.

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