
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]


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The acute angle \( A \) of rhombus \( A B C D \) is \( 45^{\circ} \), and the projection of side \( A B \) onto side \( A D \) is 12. Find the distance from the center of the rhombus to side \( C D \).

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