
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
On the edges \( DA \), \( DB \), and \( DC \) of pyramid \( ABCD \), points \( K \), \( L \), and \( M \) are taken respectively, such that \( DK = \frac{1}{2} DA \), \( DL = \frac{2}{5} DB \), and \( DM = \frac{3}{4} DC \). Point \( G \) is the centroid of triangle \( ABC \). In what ratio does plane \( KLM \) divide segment \( DG \)?

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