
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
In the convex quadrilateral \( MNLQ \), the angles at vertices \( N \) and \( L \) are right angles, and \(\operatorname{tg} \angle QMN = \frac{2}{3}\). Find the diagonal \( NQ \), given that the side \( LQ \) is half the length of side \( MN \) and is 2 units longer than side \( LN \).

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