
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
a) Find the sum of the first 15 terms of an arithmetic progression with the first term equal to 0 and the common difference $\frac{1}{3}$.

b) Find the product of the first 15 terms of a geometric progression with the first term equal to 1 and the common ratio $\sqrt[3]{10}$.

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