
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
Trapezoid $EFGH$ has bases $EF = 15$ units and $GH = 25$ units. Diagonals $EG$ and $FH$ intersect at point $Y$. If the area of trapezoid $EFGH$ is $400$ square units, and the angle between $GH$ and the line parallel to it through $E$ (i.e., the angle at E) is $30^\circ$, what is the area of triangle $FYG$?

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