
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 a geometric progression \( b_{1}, b_{2}, \ldots, b_{3000} \) with all positive terms and a total sum \( S \). It is known that if all the terms with indices divisible by 3 (i.e., \( b_{3}, b_{6}, \ldots, b_{3000} \)) are increased by 40 times, the sum \( S \) will increase 5-fold. How will \( S \) change if all the terms in even positions (i.e., \( b_{2}, b_{4}, \ldots, b_{3000} \)) are increased by 3 times?

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