
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
The diagram shows two overlapping triangles: triangle \( FGH \) with interior angles \( 60^{\circ}, 30^{\circ} \), and \( 90^{\circ} \); and triangle \( EGH \), which is a right-angled isosceles triangle. What is the ratio of the area of triangle \( IFG \) to the area of triangle \( IEH \)?

A) \( 1:1 \)  
B) \( 1:\sqrt{2} \)  
C) \( 1:\sqrt{3} \)  
D) \( 1:2 \)  
E) \( 1:3 \)

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