
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 $ABCD$, with $AB = 2a$ and $AD = b$, point $M$ is at one-fourth the distance from $A$ to $B$ along $AB$ and point $N$ is the midpoint of side $BC$. 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}
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