
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 is drawn through the vertex \( M \) of an angle, intersecting the sides of the angle at points \( N \) and \( K \), and the angle bisector at point \( L \). Find the sum of the lengths of segments \( M N \) and \( M K \) if the area of quadrilateral \( M N L K \) is 25 and angle \( L M N \) is \( 30^\circ \).

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