
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 \( K, L, \) and \( M \) be the midpoints of the edges \( AD \), \( A_1B_1 \), and \( CC_1 \) respectively of a rectangular parallelepiped \( ABCDA_1B_1C_1D_1 \), where \( AB = a \), \( AA_1 = b \), and \( AD = c \). Find the ratio of the sum of the squares of the sides of triangle \( KLM \) to the square of the diagonal of the parallelepiped.

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