
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 the hexagon $ABCDEF$ in this diagram? [asy]
pair cis(real r, real t) { return (r*cos(t), r*sin(t)); }
pair a = (0, 0);
pair b = cis(1, -pi/2);
pair c = cis(sqrt(3), -pi/3);
pair d = cis(2, -pi/3 + atan(1/sqrt(2)));
pair e = cis(sqrt(8), -pi/3 + atan(1/sqrt(2)) + atan(1/sqrt(3)));
pair f = cis(3, -pi/3 + atan(1/sqrt(2)) + atan(1/sqrt(3)) + atan(1/sqrt(4)));
dot(a); dot(b); dot(c); dot(d); dot(e); dot(f);
draw(a--b--c--d--e--f--a);
draw(a--c); draw(a--d); draw(a--e);
label("$A$", a, NW);
label("$B$", b, SW);
label("$C$", c, W);
label("$D$", d, E);
label("$E$", e, NE);
label("$F$", f, N);
label("1", (a+b)/2, NW);
label("2", (b+c)/2, SW);
label("2", (c+d)/2, SW);
label("2", (d+e)/2, NE);
label("3", (e+f)/2, NE);
[/asy]

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