
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 $ABCDE$ given the following diagram? [asy]
import olympiad;
size(6cm); 

pair a = (0, 2);
pair b = (4, 2);
pair c = (4, 0);
pair d = (6, 0);
pair e = (0, 0);

draw(a--b--c--d--e--cycle);
label("$A$", a, NW);
label("$B$", b, NE);
label("$C$", c, E);
label("$D$", d, SE);
label("$E$", e, SW);

label("$4$", a + (b - a)/2, N);
label("$2$", b + (c - b)/2, E);
label("$2$", c + (d - c)/2, S);
label("$6$", e + (d - e)/2, S);

draw(rightanglemark(a, e, d));
draw(rightanglemark(e, d, c));

add(pathticks(a--b, s=6));
add(pathticks(c--d, s=6));
[/asy]
$AB = 4$, $BC = 2$, $CD = 2$, and $DE = 6$. Also, $AED$ forms a right triangle.

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