
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
What is the ratio of the area of the shaded square to the area of the large square given that the large square is divided into a grid of $25$ smaller squares each of side $1$ unit? The shaded square consists of a pentagon formed by connecting the centers of adjacent half-squares on the grid. The shaded region is not provided in a diagram but is described as occupying $5$ half-squares in the center of the large square.

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