
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
On the sides \( AB \) and \( AC \) of the acute-angled triangle \( ABC \), two equal rectangles \( AMNB \) and \( APQC \) are built outward. Find the distance between the vertices \( N \) and \( Q \) of the rectangles, if the lengths of the sides \( AB \) and \( AC \) are \( \sqrt{3} \) and 1 respectively, and the angle at vertex \( A \) of the triangle is \( 60^\circ \).

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