
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
A circle passes through the adjacent vertices \( M \) and \( N \) of rectangle \( MNPQ \). The length of the tangent drawn from point \( Q \) to the circle is 1, and \( PQ = 2 \). Find all possible values that the area of rectangle \( MNPQ \) can take if the diameter of the circle is \(\sqrt{5}\).

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