
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 a rectangle with sides \(a\) and \(b\), the angle bisectors of all the corners are drawn until they intersect. Find the area of the quadrilateral formed by the bisectors.

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