
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
Express the area of the quadrilateral determined by the midpoints of the segments \( AB \), \( BE \), \( FC \), and \( DG \), in terms of \( a \) and \( b \), given that \( A B C D \) is a square with side length \( a \), and \( B E F G \) is a square with side length \( b \).

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