
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
On the sides \( AB \) and \( AD \) of the rectangle \( ABCD \), points \( M \) and \( N \) are marked, respectively. It is known that \( AN = 3 \), \( NC = 39 \), \( AM = 10 \), and \( MB = 5 \).

(a) (1 point) Find the area of the rectangle \( ABCD \).

(b) (3 points) Find the area of the triangle \( MNC \).

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