
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
An $10$-cm-by-$10$-cm square has diagonals drawn from each vertex to the opposite vertex. Points $A$ and $B$ are located 2 cm away from the top left and bottom right corners along the top and bottom edges, respectively. A line segment is drawn from point $A$ to the midpoint of the diagonal closest to $B$ (3 cm from one end). Calculate the area of the region shaded that includes the midpoint and A, and is bounded by the two diagonal lines.

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