
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 S<sub>n</sub> be the sum of the first n terms of the sequence {a<sub>n</sub>}. If $$\frac {S_{2n}}{S_{n}}$$ (n∈N<sup>\*</sup>) is a non-zero constant, then the sequence is called a "sum-geometric sequence". If the sequence {C<sub>n</sub>} is an arithmetic sequence with first term C<sub>1</sub> and common difference d (d≠0), and the sequence {C<sub>n</sub>} is a "sum-geometric sequence", find the relationship between d and C<sub>1</sub>.

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