
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 diagram shows a square \(KLMN\). A second square \(PQRS\) is drawn inside it, where \(P\) divides the side \(KL\) in the ratio \(1:2\). Similarly, a third square \(TUVW\) is drawn inside \(PQRS\) with \(T\) dividing \(PQ\) in the ratio \(1:2\). What fraction of the area of \(KLMN\) is shaded?

A) \(\frac{25}{81}\)

B) \(\frac{16}{49}\)

C) \(\frac{4}{9}\)

D) \(\frac{40}{81}\)

E) \(\frac{2}{3}\)

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