
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
Find the first term and the common ratio of an infinitely decreasing geometric progression if the ratio of the sum of the cubes of all its terms to the sum of all its terms is $\frac{48}{7}$, and the ratio of the sum of the fourth powers of the terms to the sum of the squares of the terms is $\frac{144}{17}$.

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