
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
Square \( ABCD \) has area \( 144 \). Point \( E \) lies on side \( \overline{BC} \). Points \( F \) and \( G \) are the midpoints of \( \overline{AE} \) and \( \overline{DE} \), respectively. Given that quadrilateral \( BEGF \) has area \( 50 \), what is the area of triangle \( GCD \)?

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