
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 sequence with a non-zero first term and a non-zero common ratio, and an arithmetic sequence with a first term equal to 0, find the sum of the first ten terms of the sequence formed by adding the corresponding terms of the first two sequences.

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