
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
Given two groups of numerical sequences, each containing 15 arithmetic progressions with 10 terms each. The first terms of the progressions in the first group are $1, 2, 3, \ldots, 15$, and their differences are respectively $2, 4, 6, \ldots, 30$. The second group of progressions has the same first terms $1, 2, 3, \ldots, 15$, but the differences are respectively $1, 3, 5, \ldots, 29$. Find the ratio of the sum of all elements of the first group to the sum of all elements of the second group.

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