
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 the triangle \( FGH \), we can draw a line parallel to its base \( FG \), through point \( X \) or \( Y \). The areas of the shaded regions are the same. The ratio \( HX : XF = 4 : 1 \). What is the ratio \( HY : YF \)?

A) \(1 : 1\)

B) \(2 : 1\)

C) \(3 : 1\)

D) \(3 : 2\)

E) \(4 : 3\)

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