
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 $\left\{a_{n}\right\}$ is an arithmetic sequence with a common difference $d (d \neq 0)$, and $a_{1}+t^{2}=a_{2}+t^{3}=a_{3}+t$.

(1) Determine the values of the real numbers $t$ and $d$.

(2) If positive integers satisfy $m < p < r$, and $a_{m} - 2t^{m} = a_{p} - 2t^{p} = a_{r} - 2t^{r} = 0$, find the array $(m, p, r)$ and the corresponding general term formula $a_{n}$.

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