
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 $a_1$ and $d$ be real numbers, and let $\{a_n\}$ be an arithmetic sequence with the first term $a_1$ and common difference $d$. The sum of the first $n$ terms of this sequence is denoted as $S_n$, satisfying $S_5S_6+15=0$.

(Ⅰ) If $S_5 \neq 5$, find $S_6$ and $a_1$;  
(Ⅱ) Determine the range of values for $d$.

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