
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 the diagram, $\triangle ABE$, $\triangle BCE$, and $\triangle CDE$ are right-angled, with $\angle AEB=\angle BEC = \angle CED = 60^\circ$, and $AE=30$. [asy]
pair A, B, C, D, E;
A=(0,25.981);
B=(0,0);
C=(11.25, -6.495);
D=(16.875, -3.2475);
E=(15,0);
draw(A--B--C--D--E--A);
draw(B--E);
draw(C--E);
label("A", A, N);
label("B", B, W);
label("C", C, SW);
label("D", D, dir(0));
label("E", E, NE);
[/asy] Find the perimeter of quadrilateral $ABCD.$

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