
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 rectangle $ABCD$, point $M$ is positioned one-third the way along side $AB$ from $A$ to $B$ and point $N$ is positioned a quarter along side $BC$ from $B$ to $C$. What is the ratio of the area of triangle $AMN$ to the area of rectangle $ABCD$?

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