
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 sequence $\{a\_n\}$ that satisfies $a\_1=10$, $a\_n-10\leqslant a\_{n+1}\leqslant a\_n+10 (n\in\mathbb{N}^*)$.

(1) If $\{a\_n\}$ is an arithmetic sequence, $S\_n=a\_1+a\_2+...+a\_n$, and $S\_n-10\leqslant S\_{n+1}\leqslant S\_n+10 (n\in\mathbb{N}^*)$, find the set of possible values for the common difference $d$;

(2) If $b\_1$, $b\_2$, ..., $b\_k$ form a geometric sequence with common ratio $q$ being an integer greater than 1, $b\_1=10$, $b\_2\leqslant 20$, and $b\_1+b\_2+...+b\_k > 2017$, find the minimum value of the positive integer $k$.

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