
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 of side length 60 units, subdivided into a grid with non-uniform rows and columns. The rows are divided into segments of 20, 20, and 20 units, and the columns are divided into segments of 15, 15, 15, and 15 units. A shaded region is created by connecting the midpoint of the leftmost vertical line to the midpoint of the top horizontal line, then to the midpoint of the rightmost vertical line, and finally to the midpoint of the bottom horizontal line. What is the ratio of the area of this shaded region to the area of the large square?

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