
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 \(\left\{a_{n}\right\}\) such that \(a_{1}=2t-3\) (\(t \in \mathbf{R}\) and \(t \neq \pm 1\)),
\[
a_{n+1}=\frac{\left(2t^{n+1}-3\right)a_{n}+2(t-1)t^{n}-1}{a_{n}+2t^{n}-1} \left(n \in \mathbf{N}^{*}\right).
\]
(1) Find the general term 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}
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