
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
Let  $ABC$  be a triangle with  $AB=3$ ,  $BC=4$ , and  $CA=5$ . The line through  $A$  perpendicular to  $AC$  intersects line  $BC$  at  $D$ , and the line through  $C$  perpendicular to  $AC$  intersects line  $AB$  at  $E$ . Compute the area of triangle  $BDE$ .


*2021 CCA Math Bonanza Lightning Round #2.1*

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