
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
Let $ABCD$ be a rectangle where $AB = 4$ and $AD = 2$. Let $M$ and $N$ be the midpoints of $\overline{AD}$ and $\overline{BC}$ respectively. Find $\sin \theta$ where $\theta$ is the angle formed between the diagonal $\overline{AC}$ and the segment $\overline{MN}$.

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