
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

A circle passes through vertex $B$ of triangle $ABC$, touches side $AC$ at its midpoint $D$, and intersects sides $AB$ and $BC$ at points $M$ and $N$ respectively. Given that $AB:BC=3:2$, find the ratio of the area of triangle $AMD$ to the area of triangle $DNC$.

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