
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 sequence \(\left\{a_{n}\right\}\) that satisfies: \(a_{1}=2 t-2(t \in \mathbf{R} \text{ and } t \neq \pm 1)\),

\[ a_{n+1}=\frac{2\left(t^{n+1}-1\right) a_{n}}{a_{n}+2 t^{n}-2} \quad (n \in \mathbf{N}^{*}) \]

(1) Find the general term formula for the sequence \(\left\{a_{n}\right\}\);

(2) If \(t>0\), compare the sizes of \(a_{n+1}\) and \(a_{n}\).

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