
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 following diagram, triangles $\triangle ABE$, $\triangle BCE$ contain right angles at B and C, with $\angle AEB = \angle BEC = 45^\circ$, and $AE=30$. [asy]
pair A, B, C, D, E;
A=(0,21.2132);
B=(0,0);
C=(15,0);
D=(20,0);
E=(30,0);
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, SE);
label("E", E, NE);
[/asy] Calculate the area of triangle $ABE$.

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