
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
The sum of the first \( n \) terms of a geometric sequence \(\left\{a_{n}\right\}\) with all real numbers is \( S_{n} \). If \( S_{10} = 10 \) and \( S_{30} = 70 \), calculate \( S_{40} \).

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