
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
Consider a large square and a smaller square formed by joining the midpoints of the sides of the larger square. Additionally, a right triangle is formed by connecting a vertex of the larger square to the midpoint of an adjacent side and the center of the square. If the area of the larger square is 100 square units, what is the area of the smaller square and the right triangle?

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