
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 $\triangle{ABC}$, $AB = 15$, $\angle{A} = 45^\circ$, and $\angle{C} = 30^\circ$. Let $H$ be the foot of the perpendicular from $A$ to $BC$, $M$ be the midpoint of $BC$, and $D$ be the point on $BC$ such that $\angle{BAD} = \angle{CAD}$. Place point $N$ at the midpoint of segment $HM$. Find the area of triangle $AMN$.

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