
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
In a new diagram, what is the perimeter of polygon $ABCDE$? Diagram below:
\[ \text{[asy]}
import olympiad;
size(6cm); // ADJUST

pair a = (0, 5);
pair b = (4, 5);
pair c = (4, 2);
pair d = (0, 0);
pair e = (10, 0);

draw(a--b--c--e--d--cycle);
label("$A$", a, N);
label("$B$", b, N);
label("$C$", c, E);
label("$D$", d, W);
label("$E$", e, S);

label("$5$", a / 2, W);
label("$3$", b + (c - b) / 2, 2 * N);
label("$10$", e / 2, S);

draw(rightanglemark(b, a, d));
draw(rightanglemark(d, a, b));
draw(rightanglemark(a, b, c));
add(pathticks(a--b, s=6));
add(pathticks(b--c, s=6));
\text{[/asy]} \]

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