
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 rectangle $ABCD$, $\overline{AB} = 30$ and $\overline{BC} = 15$. Let $E$ be a point on $\overline{CD}$ such that $\angle CBE = 30^\circ$. Find the length of segment $\overline{AE}$.
A) $15\sqrt{2}$
B) $25$
C) $30$
D) $35$
E) $45$

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