
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 line \( MN \) parallel to the base \( AB \) is drawn through the center of the circle inscribed in triangle \( ABC \) (\(M\) lies on \( BC \), \(N\) on \( AC \)). Find the perimeter of the quadrilateral \( ABMN \), given that \( AB = 5 \) and \( MN = 3 \).

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