
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
Find the positions of points \( N \) on side \( AC \) and \( M \) on side \( BC \) of an isosceles triangle \( ABC \) such that \( MN \parallel AB \) and the sum \( AM + MN + NB \) is minimized.

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