
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 $\triangle ABC$ with $\angle BAC = 90^\circ$, angle bisectors $BD$ and $BE$ of $\angle ABC$ and $\angle BCA$, respectively, intersect at point $E$. If the area of $\triangle BDE$ is $L$, find the area of $\triangle ABC$.
A) $2L$
B) $4L$
C) $3L$
D) $L$
E) $\frac{L}{2}$

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