
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 $a_1$ and $d$ as real numbers, for an arithmetic sequence $\{a_n\}$ with the first term $a_1$ and common difference $d$, let the sum of the first $n$ terms be $S_n$. It is known that $S_5 \cdot S_6 + 15 = 0$.
1. If $S_5 \neq 5$, find the general term formula for $\{a_n\}$.
2. For another sequence $\{b_n\}$ with the sum of the first $n$ terms denoted by $T_n$, and $T_n = a_n^2$, find the general term formula for $\{b_n\}$.

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