
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 circle of radius 1 touching three sides of a \(2 \times 4\) rectangle. A diagonal of the rectangle intersects the circle at \(P\) and \(Q\), as shown. What is the length of the chord \(PQ\)?

A) \(\sqrt{5}\)
B) \(\frac{4}{\sqrt{5}}\)
C) \(\sqrt{5} - \frac{2}{\sqrt{5}}\)
D) \(\frac{5 \sqrt{5}}{6}\)
E) 2

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