
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
Points \( M \) and \( N \) are the midpoints of the sides \( AC \) and \( CB \) of the isosceles triangle \( ACB \). Point \( L \) lies on the median \( BM \) such that \( BL : BM = 4 : 9 \). A circle with center at point \( L \) is tangent to the line \( MN \) and intersects the line \( AB \) at points \( Q \) and \( T \). Find the perimeter of the triangle \( MNC \) if \( QT = 2 \) and \( AB = 8 \).

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