
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 $AN = 11$, $NC = 39$, $AM = 12$, 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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