
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
Rectangle $ABCD$ has sides $AB=4$ and $BC=2$. Let $M$ be the midpoint of $\overline{BC}$, and let $N$ be the point on $\overline{CD}$ so that $CN = \frac{1}{4}CD$. Find $\sin \theta$, where $\theta$ is the angle between $\overline{AM}$ and $\overline{AN}$.

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