
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
The plane is tiled by congruent squares and congruent pentagons. Each large square is divided into a $4 \times 4$ grid of smaller squares. Ten of these smaller squares, either fully or partially, contribute to the formation of the pentagons. What is the ratio of the area of the pentagons to the area of the entire plane?

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