
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 \(\left\{a_{n}\right\}\) satisfies: \(a_{1}=2 t-3\) (where \(t \in \mathbf{R}\) and \(t \neq \pm 1\)),
\[ a_{n+1}=\frac{\left(2 t^{n+1}-3\right) a_{n}+2(t-1) t^{n}-1}{a_{n}+2 t^{n}-1} \quad (n \in \mathbf{N}^{*}) \]

1. Find the general term formula of the sequence \(\left\{a_{n}\right\}\);
2. If \(t>0\), compare \(a_{n+1}\) and \(a_{n}\).

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