
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
Square \( A B C D \) has sides of length \( 3 \text{ cm} \). The points \( M \) and \( N \) lie on \( A D \) and \( A B \) so that \( C M \) and \( C N \) split the square into three pieces of the same area. What is the length of \( D M \)?

A) \( 0.5 \text{ cm} \)  
B) \( 1 \text{ cm} \)  
C) \( 1.5 \text{ cm} \)  
D) \( 2 \text{ cm} \)  
E) \( 2.5 \text{ cm} \)

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