
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
Points $P$, $Q$, $R$, and $S$ are midpoints of the sides of a larger square. If the larger square has an area of 100 square units, what is the area of the smaller square formed by connecting these midpoints?

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