
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 trapezoid $ABCD$, the sides $AB$ and $CD$ are parallel. Let $M$ be the midpoint of the diagonal $AC$, $N$ the midpoint of the diagonal $BD$, and $P$ the midpoint of the side $AB$. Given that $AB = 15 \text{ cm}$, $CD = 24 \text{ cm}$, and the height of the trapezoid is $h = 14 \text{ cm}$:

a) Calculate the length of the segment $MN$.

b) Calculate the area of the triangle $MNP$.

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