
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 the arithmetic sequence $\{a\_n\}$ with the sum of its first $n$ terms being $S\_n=2n^{2}-4n+c$, find the first term $a\_1=$ \_\_\_\_\_\_; and the relationship between the first term $a\_1$ and common difference $d$ that satisfies $(a\_1)^{d}=$ \_\_\_\_\_\_.

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