
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 $10$-cm-by-$10$-cm square is divided into four right triangles by drawing its diagonals. Points $P$ and $Q$ are the midpoints of two adjacent sides of the square. Calculate the area of the quadrilateral formed by connecting the midpoint of one side of the square, the center, and the midpoints of the adjacent sides.

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