
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 that $\{a_n\}$ is an arithmetic sequence with a nonzero common difference and $\{b_n\}$ is a geometric sequence satisfying $b_1=a_1^2$, $b_2=a_2^2$, $b_3=a_3^2$:

(Ⅰ) Find the common ratio $q$ of the geometric sequence $\{b_n\}$;
(Ⅱ) If $a_2=-1$ and $a_1<a_2$, find the common difference of the arithmetic sequence $\{a_n\}$.

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