
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 large square is divided into a grid of 36 smaller equal squares, and a particular configuration in the grid shapes a shaded triangular region. The shaded triangular area is formed by connecting the midpoint of one side of the large square to the diagonal corner of the 4x4 square block located in one corner of the large square and to the midpoint of the adjacent side. What is the ratio of the area of this shaded triangular region to the area of the large square?

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