
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
Let \( a_{1}, a_{2}, a_{3}, \cdots \) be a sequence of real numbers in a geometric progression. Let \( S_{n} = a_{1} + a_{2} + \cdots + a_{n} \) for all integers \( n \geq 1 \). Assume that \( S_{10} = 10 \) and \( S_{30} = 70 \). Find the value of \( S_{40} \).

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