
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
A rectangle has dimensions $a$ units by $b$ units. Within this rectangle, a smaller rectangle is positioned such that its sides are parallel to the sides of the larger rectangle, and it has dimensions $u$ units by $v$ units. The remaining area of the larger rectangle is divided into four congruent right triangles by lines connecting the vertices of the smaller rectangle to the midpoints of the sides of the larger rectangle. What is the area of one of these four right triangles? Express your answer in terms of $a$, $b$, $u$, and $v$.

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