
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
Two congruent 30-60-90 triangles are placed with their 60-degree angles overlapping, and the hypotenuse of each triangle is 10 units. Calculate the area common to both triangles.
A) $40\sqrt{3}$  
B) $45\sqrt{3}$  
C) $50\sqrt{3}$  
D) $60\sqrt{3}$  
E) $55\sqrt{3}$

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