
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 rectangle \(ABCD\), points \(M\) and \(N\) are marked, respectively. It is known that \(AN=7\), \(NC=39\), \(AM=12\), and \(MB=3\).

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

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

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