
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 pentagon $ABCDE$ in the diagram below? [asy]
pair cis(real r, real t) { return (r*cos(t), r*sin(t)); }
pair a = (0, 0);
pair b = cis(2, -pi/2);
pair c = cis(sqrt(5), -pi/4);
pair d = cis(sqrt(8), -pi/4 + atan(1/2));
pair e = cis(3, -pi/4 + atan(1/2) + atan(1/sqrt(3)));
dot(a); dot(b); dot(c); dot(d); dot(e);
draw(a--b--c--d--e--a);
draw(a--c); draw(a--d);
draw(0.86*b--0.86*b + 0.14*(c-b)--b + 0.14*(c-b));
draw(0.9*c--0.9*c + 0.14*(d-c)--c + 0.14*(d-c));
draw(0.92*d--0.92*d + 0.14*(e-d)--d + 0.14*(e-d));
label("$A$", a, NW);
label("$B$", b, SW);
label("$C$", c, SSE);
label("$D$", d, ESE);
label("$E$", e, NE);
label("2", (a+b)/2, W);
label("$\sqrt{5}$", (b+c)/2, S);
label("$\sqrt{3}$", (c+d)/2, SE);
label("$\sqrt{5}$", (d+e)/2, E);
[/asy]

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